## Archive of Interior-Point Papers

By clicking on the paper title, you will see an abstract with links to the postscript and/or dvi versions of the paper. You can retrieve the whole paper by clicking on one of these links.

Usually, the paper will be retrieved directly from the authors' ftp site, so that you will always be accessing the most current version. It is the authors' responsibility to make sure the file stays where they said it was in their original announcement. They need to let us know if it is deleted, moved, or renamed, since these actions will cause the link to go dead.

You can also SEARCH THE ARCHIVE, by author name:

Wang, Y. and Monteiro, R.D.C.,
"Nondegeneracy of polyhedra and linear programs," working paper, August 1994.

Andersen, K. D.
"A modified Schur complement for handling dense columns in interior point methods for linear programming," December, 1994; revised October, 1995.

Todd, M. J. and Ye, Y.
"Approximate Farkas Lemmas and Stopping Rules for Iterative Infeasible-Point Algorithms for Linear Programming," Technical Report No. 1109, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801

Jie Sun, Jishan Zhu, and Gongyun Zhao,
"A primal-dual affine scaling algorithm with necessary centering as a safeguard," Technical Report No. 647, Department of Mathematics, National University of Singapore.

Vanderbei, R. J., Duarte, A., and Yang, B.,
"An Algorithmic and Numerical Comparison of Several Interior-Point Methods," Technical Report SOR-94-05, Program in Statistics and Operations Research, Princeton University, July, 1994.

Portugal, L. and Judice, J.
"A hybrid algorithm for the solution of a single commodity spatial equilibrium model," (no report number supplied).

Zhao Gong Yun and Zhuangwei Liu
"A line-search method for Lagrangian relaxation ascent algorithms," Technical Report No. 644, Department of Mathematics, National University of Singapore, 0511, SINGAPORE

Stephen A. Vavasis and Yinyu Ye
"A Primal-Dual Accelerated Interior Point Method Whose Running Time Depends Only on $A$,"

Gongyun Zhao
"High-order large-step interior point algorithms for linear complementarity problems," Technical Report No. 650, Department of Mathematics, National University of Singapore, 0511, SINGAPORE

Florian A. Potra and J. Frédéric Bonnans
"Infeasible path following algorithms for linear complementarity problems," INRIA Research Report RR-2445, December 1994.

Masakazu Kojima
"A primitive interior-point algorithm for semidefinite programs in Mathematica," Research Reports on Information Sciences B-293, December 1994.

R.W. Freund, F. Jarre and S. Schaible
"On interior-point methods for fractional programs and their convex reformulation," AT&T Numerical Analysis Manuscript No. 94-17, Bell Laboratories, Murray Hill, New Jersey, November 1994.

Jos F. Sturm and Shuzhong Zhang
"A Dual and Interior Point Approach to Solve Convex Min-Max Problems,"

Jos F. Sturm and Shuzhong Zhang
"New complexity results for the Iri-Imai method,"

Jos F. Sturm and Shuzhong Zhang
"An O(\sqrt{n}L) Iteration Bound Primal-Dual Cone Affine Scaling Algorithm for Linear Programming,"

Robert M. Freund
"Complexity of an Algorithm for Finding an Approximate Solution of a Semi-Definite Program, with no Regularity Condition"

Florian Jarre and Stephen Wright
"The Role of Linear Objective Functions in Barrier Methods," Preprint MCS-P485-1294, MCS Division, Argonne National Laboratory. (Revised, August, 1997.)

Stephen Wright and Yin Zhang
"A Superquadratic Infeasible-Interior-Point Method for Linear Complementarity Problems," Research Report YZ94-03, Department of Mathematics and Statistics, UMBC Preprint MCS-P418-0294, MCS Division, Argonne National Laboratory (February, 1994. Revised November, 1994.)

Yin Zhang
LIPSOL version 0.3 Release Announcement.

Michael Todd
"Potential-Reduction Methods in Mathematical Programming," Technical Report No. 1112, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801

Masakazu Kojima, Masayuki Shida and Susumu Shindoh
"Reduction of monotone linear complementarity problems over cones to linear programs over cones," Research Reports on Information Sciences B-296, Feb. 1995

Knud D. Andersen and Edmund Christiansen
"A Newton barrier method for minimizing a Sum of Euclidean norms subject to linear equality constraints," Preprint 95-07, Department of Mathematics and Computer Science, Odense University, Denmark. February, 1995.

R.W. Freund and F. Jarre
"A QMR-based interior-point algorithm for solving linear programs," AT&T Numerical Analysis Manuscript No. 94-19, Bell Laboratories, Murray Hill, New Jersey, December 1994.

Robert Vanderbei
"LOQO: An Interior Point Code for Quadratic Programming," Technical Report SOR 94--15, Program in Statistics & Operations Research, Princeton University, February 1995.

Patricia D. Hough and Stephen A. Vavasis
"Complete Orthogonal Decomposition for Weighted Least Squares," Preprint, Cornell University, March, 1995.

T. Tsuchiya and Renato D. C. Monteiro,
"Superlinear convergence of the affine scaling algorithm," SIE Working Paper 92-27, SIE Department, University of Arizona, Tucson, AZ 85721, November 1992.

Renato D. C. Monteiro and T. Tsuchiya
"Global Convergence of the Affine Scaling Method for Convex Quadratic Programming," Preprint, Georgia Institute of Technology, March, 1995.

Anders Forsgren
"On linear least-squares problems with diagonally dominant weight matrices," SIAM Journal on Matrix Analysis and Applications 17 (1996), 763-788.

M. Anitescu, G. Lesaja, F. Potra
"An infeasible--interior--point predictor--corrector algorithm for the $P_*$-Geometric LCP," Reports on computational mathematics, No. 62/1994, Department of Mathematics, The University of Iowa

F. Alizadeh, J.-P. A. Haeberly and M.L. Overton
"Complementarity and Nondegeneracy in Semidefinite Programming"

Erling D. Andersen and Yinyu Ye
"On a Homogeneous Algorithm for the Monotone Complementarity problem"

Knud D. Andersen and Edmund Christiansen
"A symmetric Primal-Dual Newton method for minimizing sum of norms"

Florian A. Potra and Rongqin Sheng
"A path following method for LCP with superlinearly convergent iteration sequence," Reports on Computational Mathematics, No. 69, Department of Mathematics, University of Iowa, April, 1995.

Masakazu Kojima, Susumu Shindoh, Shinji Hara
"Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices," Research Reports on Information Sciences, No. B-282, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, April, 1994, Revised April 1995.

Jacek Gondzio
"Presolve Analysis of Linear Programs Prior to Applying an Interior Point Method," Technical Report 1994.3, Logilab, HEC Geneva, Section of Management Studies, University of Geneva, Bd. Carl-Vogt 102, 1211 Geneva, Switzerland, February 1994, revised December 1994.

Jacek Gondzio
"Multiple Centrality Corrections in a Primal--Dual Method for Linear Programming," Technical Report 1994.20, Logilab, HEC Geneva, Section of Management Studies, University of Geneva, Bd. Carl-Vogt 102, 1211 Geneva, Switzerland, November 1994, revised May 1995.

David Shanno and Evangelia Simantiraki
"An Infeasible Interior-Point Method for Linear Complementarity Problems," Rutcor Research Report 7--95, March 1995 (revised, February, 1996).

Yu.E. Nesterov and M.J. Todd
"Primal-Dual Interior-Point Methods for Self-Scaled Cones," Technical Report No. 1125, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801.

Irvin J. Lustig and Edward Rothberg
"Gigaflops in Linear Programming," Manuscript, CPLEX Optimization, Inc. and Silicon Graphics, Inc., May, 1995.

A. S. El-Bakry, R. A. Tapia and Y. Zhang
"On the Convergence Rate of Newton Interior-Point Methods in the Absence of Strict Complementarity," Technical Report, revised May, 1995.

M. Ramana, L. Tuncel and H. Wolkowicz
"Strong duality for semidefinite programming," CORR 95-12, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, June 1995.

T. Fujie and M. Kojima
"Relaxation by Semidefinite Programs," Research Reports on Information Sciences, No. B-298, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, May 1995, Revised August 1996, to appear in Journal of Global Optimization.

O. Guler and L. Tuncel
"Characterization of the barrier parameter of homogeneous convex cones," Research Report CORR 95-14, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, June 1995.

Mihai Anitescu, Lesaja Goran , Florian A. Potra
"Equivalence between different formulations of the linear complementarity problem," Reports on Computational Mathematics, No.71, Department of Mathematics, The University of Iowa, June 1995.

Guoliang Xue and Yinyu Ye
"An efficient algorithm for minimizing a sum of Euclidean norms with applications," University of Vermont Research Report, CSEE/95/06-01, Department of Computer Science and Electrical Engineering, The University of Vermont, June 1995.

Jos F. Sturm and Shuzhong Zhang
"On a wide region of centers and primal-dual interior point algorithms for linear programming," Report 9520/A, Econometric Institute, Erasmus University Rotterdam, Rotterdam, The Netherlands.

L. Faybusovich and J.B. Moore
"Infinite dimensional quadratic optimization: interior-point methods and control applications Preprint," Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden, January, 1995.

Stephen J. Wright
"Stability of Augmented System Factorizations in Interior-Point Methods," (revision of "Stability of Linear Algebra Computations in Interior-Point Methods for Linear Programming") Preprint MCS-P446-0694, June, 1994; revised July 1995.

Srinivasan Ramaswamy and John E. Mitchell
"A Long Step Cutting Plane Algorithm That Uses the Volumetric Barrier," June 1995.

R.D.C. Monteiro and F. Zhou,
"On superlinear convergence of infeasible-interior-point algorithms for linearly constrained convex programs," working paper, July 1995.

R.D.C. Monteiro and Y. Wang,
"Trust region affine scaling algorithms for linearly constrained convex and concave programs," working paper, June 1995.

T. Wang, R.D.C. Monteiro, and J.--S. Pang,
"An interior point potential reduction method for constrained equations algorithms for linearly constrained convex and concave programs," working paper, June 1995.

Osman Guler,
"On the Self-Concordance of the Universal Barrier Function," Technical Report GU 95-2, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21228-5398.

M. Shida, S. Shindoh and M. Kojima,
"Centers of Monotone Generalized Complementarity Problems," Research Reports on Information Sciences B-303, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, August 1995.

R.D.C. Monteiro
"Primal-Dual Path Following Algorithms for Semidefinite Programming," working paper, September 1995.

L. Tuncel and M. J. Todd
"On the interplay among entropy, variable metrics and potential functions in interior-point algorithms," Research Report CORR 95-20, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, September 1995. Also available as Technical Report 1135, School of OR and IE, Cornell University, Ithaca, NY, September 1995.

L. Portugal, J. Judice, and L. Fernandez
"A truncated Newton interior-point algorithm for the solution of a multicommodity spatial equilibrium model," Working paper, October, 1995.

Evangelia Simantiraki and David F. Shanno
"An infeasible-interior-point method for solving mixed complementarity problems," RUTCOR Research Report 37--95, September, 1995.

J. Sun, K.-E. Wee, J.-S. Zhu
"An Interior Point Method for Solving a Class of Linear-Quadratic Stochastic Programming Problems," Recent Advances in Nonsmooth Optimization Editors D.-Z. Du, Liqun Qi, R.S. Womersley, (World Scientific, Singapore, 1995) 392-404.

Jie Sun
"Convergence Analysis for a Convex Version of Dikin's Algorithm," To appear in Annals of Operations Research.

J. Sun, J. Zhu, G. Zhao
"A Predictor-Corrector Algorithm for a Class of Nonlinear Saddle Point Problems," To appear in SIAM Journal on Control and Optimization.

Y. Zhang
"On Extending Primal-dual Interior-Point Algorithms From Linear Programming To Semidefinite Programming," Technical Report TR95-20, Department of Mathematics and Statistics, University of Maryland Baltimore County, November, 1995.

Z-Q Luo and P. Tseng
"A New Class of Merit Functions for the Nonlinear Complementarity Problem," Technical Report.

S. Mehrotra and J-S Wang
"Conjugate Gradient Based Implementation of Interior Point Methods for Network Flow Problems," Technical Report 95-70, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, October, 1995.

J. Ji and F. Potra
"Tapia indicators and finite termination of infeasible--interior--point methods for degenerate LCP," Reports on Computational Mathematics, No. 81/1995, Department of Mathematics, The University of Iowa.

M. Kojima, M. Shida and S. Shindoh
"Local Convergence of Predictor-Corrector Infeasible-Interior-Point Algorithms for SDPs and SDLCPs," Technical Report, October, 1995; revised December, 1995.

Chih-Jen Lin and Romesh Saigal
"A predictor-corrector method for for semidefinite linear programming," Technical Report, Department of Industrial Engineering, University of Michigan, October, 1995.

F. A. Potra and Rongqin Sheng
"A superlinearly convergent primal-dual infeasible-interior-point algorithm for semidefinite programming," Reports on Computational Mathematics, No.78, Department of Mathematics, The University of Iowa, October 1995.

Robert M. Freund and Jorge R. Vera
"Some Characterizations and Properties of the 'Distance to Ill-Posedness' and the Condition Measure of a Conic Linear System," Technical Report, October, 1995.

C. Helmberg, F. Rendl, R. J. Vanderbei and H. Wolkowicz
"An interior point method for semidefinite programming," Research Report, University of Waterloo. To appear in SIOPT.

O. Guler
"Hyperbolic Polynomials and Interior Point Methods for Convex Programming," Technical Report TR95-40, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21228-5398.

L. Faybusovich
"Jordan algebras, Symmetric cones and Interior-point methods," Research Report,October, 1995, University of Notre Dame, Notre Dame, USA.

Y. Ye
"On the complexity of approximating a KKT point of quadratic programming," Working Paper.

Z.-Q. Luo and J. Sun
"An Analytic Center Based Column Generation Algorithm For Convex Quadratic Feasibility Problems."

Cs. Meszaros
"The inexact'' minimum local fill-in ordering algorithm," Working Paper WP 95-7, Computer and Automation Institute, Hungarian Academy of Sciences, Budapest.

F. Potra and R. Sheng
"Homogeneous Interior--Point Algorithms for Semidefinite Programming," Reports On Computational Mathematics, No. 82/1995, Department Of Mathematics, The University Of Iowa.

Cs. Meszaros
"The augmented system variant of IPMs in two--stage stochastic linear programming computation," Working Paper WP 95-11, Computer and Automation Institute, Hungarian Academy of Sciences, Budapest.

Katsuki Fujisawa and Masakazu Kojima
"SDPA (Semidefinite Programming Algorithm)," Software package. User's manual is Research Report on Information Sciences B-308, Tokyo Institute of Technology, December, 1995.

Franz Rendl and Christoph Helmberg
"Solving Quadratic (0,1)-Problems by Semidefinite Programs and Cutting Planes," Preprint SC-95-35 of the Konrad-Zuse-Zentrum fuer Informationstechnik Berlin.

Stefan E. Karisch and Franz Rendl
"Semidefinite Programming and Graph Equipartition," Report 302 - CDLDO 55, Department of Mathematics, Graz University of Technology, Graz, Austria, December 1995.

Romesh Saigal and C. J. Lin
"An infeasible start predictor corrector method for semi-definite linear programming," Dec 1995.

Benjamin Jansen, Kees Roos, Tam\'{a}s Terlaky and Akiko Yoshise
"Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems," Technical Report 95-83, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands, September, 1995.

Jie Sun and Gongyun Zhao
"A quadratically convergent polynomial long-step algorithm for a class of nonlinear monotone complementarity problems," National Univ. of Singapore, January, 1996.

Kurt M. Anstreicher and Marcia Fampa
"A Long-Step Path Following Algorithm for Semidefinite Programming Problems," University of Iowa, January 1996.

Daniel Ralph and Stephen Wright
"Superlinear Convergence of an Interior-Point Method for Monotone Variational Inequalities," Research Report No. 3, 1996, Department of Mathematics, University of Melbourne; Preprint MCS-P556-0196, Mathematics and Computer Science Division, Argonne National Lab.

Yinyu Ye
"Convergence behavior of the central path for homogeneous and self-dual cones," unpublished note.

Masayuki Shida, Susumu Shindoh and Masakazu Kojima
"Existence of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP," Research Report B-310, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo 152 Japan, January 1996.

M. Kojima, M. Shida and S. Shindoh
"A Predictor-Corrector Interior-Point Algorithm for the Semidefinite Linear Complementarity Problem Using the Alizadeh-Haeberly-Overton Search Direction," Research Report B-311, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo 152, Japan, January 1996.

Edward Rothberg and Bruce Hendrickson
"Sparse Matrix Ordering Methods for Interior Point Linear Programming," Manuscript, January 1996.

Erling D. Andersen, Jacek Gondzio, Csaba Mészáros and Xiaojie Xu
"Implementation Of Interior Point Methods For Large Scale Linear Programming," Technical Report 1996.3, Logilab, HEC Geneva, Section of Management Studies, University of Geneva, 102 Bd Carl-Vogt, CH-1211, Switzerland.

Zhi-Quan Luo, Jos Sturm, and Shuzhong Zhang
"Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming," Report 9607/A, Econometric Institute, Erasmus University, Rotterdam.

Jos F. Sturm and Shuzhong Zhang
"Symmetric primal-dual path following algorithms for semidefinite programming," Report 9554/A, Econometric Institute, Erasmus University, Rotterdam.

Kurt M. Anstreicher
"Potential Reduction Algorithms," to appear in Interior Point Methods in Mathematical Programming, T. Terlaky, editor, Kluwer, 1996.

Yin Zhang
"Solving Large-Scale Linear Programs by Interior-Point Methods Under the MATLAB Environment," Technical Report, Mathematics Department, University of Maryland Baltimore County, March, 1996.

Don Goldfarb and Katya Scheinberg
"Interior Point Trajectories in Semidefinte Programming," Technical Report, Department of IE/OR, Columbia University, New York, March, 1996. Revised November, 1996.

Arjan B. Berkelaar, Benjamin Jansen, Kees Roos, Tamas Terlaky
"Sensitivity Analysis for Degenerate Quadratic Programming," Technical Report, February, 1996.

Arjan B. Berkelaar, Benjamin Jansen, Kees Roos, and Tamas Terlaky
"Optimal Basis and Optimal Tripartition Identification Algorithms for Quadratic Programming and Linear Complementarity Problems-- from an interior solution to a basis solution and viceversa," Technical Report, March, 1996.

Jie Sun and Gongyun Zhao
"Global linear and local quadratic convergence of a long-step adaptive-mode interior point method for some monotone variational inequality problems," Technical Report, March, 1996.

Michael Todd, Kim Toh, and Reha Tutuncu
"On the Nesterov-Todd direction in semidefinite programming," Technical Report No. 1154, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, N.Y., March, 1996.

Reha Tutuncu
"An Infeasible-Interior-Point Potential-Reduction Algorithm for Linear Programming," Technical Report No. 1136, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, N.Y.

J.P. Warners, T. Terlaky, C. Roos, B. Jansen
"Potential reduction algorithms for structured combinatorial optimization problems," Report 95-88, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, 1995.

J.P. Warners, T. Terlaky, C. Roos, B. Jansen
"A potential reduction approach to the frequency assignment problem," Report 95-98, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, 1995.

E. de Klerk, C. Roos, T. Terlaky
"Semi-definite Problems in Truss Topology Optimization," Report 95--128, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

E. de Klerk, C. Roos, T. Terlaky
"A nonconvex weighted potential function for polynomial target following methods," Report 95--127, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

E. de Klerk, C. Roos, T. Terlaky
"Initialization in semidefinite programming via a self--dual skew--symmetric embedding," Report 96--10, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1996.

T. Terlaky, J.-Ph. Vial
"Computing maximum likelihood estimators of convex density functions,"Report 95-49, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

B. Jansen, C. Roos, T. Terlaky
"A new algorithm for the computation of the smallest eigenvalue of a symmetric matrix and its eigenspace,"Report 95-70, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

H. van Maaren, T. Terlaky
"Inverse barriers and CES--functions in linear programming,"Report 95-76, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

B. Jansen, C. Roos, T. Terlaky
"A short survey on ten years interior point methods," Report 95-45, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

B. Jansen, C. Roos, T. Terlaky, A. Yoshise
"Polynomiality of primal-dual affine scaling algorithms for nonlinear monotone complementarity problems,"Report 95-83, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

Manuel A. Nunez and Robert M. Freund
"Condition Measures and Properties of the Central Trajectory of a Linear Program," Technical Report, March, 1996.

Masayuki Shida, Susumu Shindoh
"Monotone Semidefinite Complementarity Problems," Research Reports on Mathematical and Computing Sciences B-312, March 1996.

J.B.G. Frenk, J.F. Sturm, S. Zhang
"An interior point subgradient method for linearly constrained nondifferentiable convex programming," Report 9612/A, Econometric Institute, Erasmus University Rotterdam.

Zhi-Quan Luo, Jos Sturm, Shuzhong Zhang
"Duality And Self-Duality For Conic Convex Programming," Report 9620/A, Econometric Institute, Erasmus University Rotterdam.

Clovis C. Gonzaga, Hugo J. Lara
"A note on properties of condition numbers," Department of Mathematics, Federal University of Santa Catarina, Cx. Postal 5210, 88040-970 Florianopolis, SC, Brazil

Kevin McShane
"On the superlinear convergence of an O(n^3L) interior point algorithm for monotone LCP," To appear in SIAM Journal of Optimization.

Jean-Philippe Vial
"A generic path-following algorithm with a sliding constraint and its application to linear programming and the computation of analytic centers," Technical Report 1996.8, Logilab, HEC Geneva, Section of Management Studies, University of Geneva, 102 Bd Carl-Vogt, CH-1211, Switzerland.

Tamas Terlaky and Takashi Tsuchiya
"A note on Mascarenhas' counter example about global convergence of the affine scaling algorithm," Reserch Memorandum No.596, The Institute of Statistical Mathematics, Tokyo, Japan, March, 1996.

M. Kojima, M. Shida and S. Shindoh
"A Note on the Nesterov-Todd and the Kojima-Shindoh-Hara Search Directions in Semidefinite Programming," Research Report B313, Dept. of Mathematical and Computing Sciences Tokyo Institute of Technology, Meguro, Tokyo 152, Japan, April 1996

Florian A. Potra and Rongqin Sheng
"Superlinear Convergence of Interior-Point Algorithms for Semidefinite Programming," Reports on Computational Mathematics 86/1996, Department of Mathematics, The University of Iowa.

Yurii Nesterov, Yinyu Ye, and Michael Todd
"Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems," Technical Report No. 1156, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801.

Adrian S. Lewis and Michael L. Overton
"Eigenvalue Optimization," Acta Numerica 1996, pp.149-190, Cambridge University Press.

J. Sun and G. Zhao
"A quadratically convergent long-step interior-point method for nonlinear monotone variational inequality problems," Technical Report, April, 1996.

Jianmin Jiang
"A Long Step Primal-Dual Path Follow ing Method for Semidefinite Programming," Science Report 96009, Dept. of Applied Math., Tsinghua Univ., Beijing 100084, China, March, 1996.

Renato D.C.Monteiro and Jong-Shi Pang
"On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems," May, 1996.

Shinji Mizuno and Florian Jarre
"Global and Polynomial-Time Convergence of an Infeasible-Interior-Point Algorithm Using Inexact Computation," Research Memorandum 605, The Institute of Statistical Mathematics, Tokyo, Japan

Jean-Louis Goffin and Jean-Philippe Vial
"Shallow, deep and very deep cuts in the analytic center cutting plane method ," Logilab Technical Report 96.1, HEC/Management Studies, University of Geneva, Switzerland, May 15, 1996

Joe Czyzyk, Sanjay Mehrotra, and Stephen Wright
"PCx User Guide," Technical Report OTC 96/01, Optimization Technology Center, Argonne National Laboratory and Northwestern University, May, 1996.

N. Megiddo, S. Mizuno and T. Tsuchiya.
"A Modified Layered-Step Interior-Point Algorithm for Linear Programming," IBM Technical Report.

B. He, E. de Klerk, C. Roos, T. Terlaky
"Method of approximate centers for semi-definite programming," Report 96-27, Faculty of Technical Mathematics and Informatics, Delft University of Technology, 1996

E. de Klerk, C. Roos, T. Terlaky
"Polynomial Primal-dual Affine Scaling Algorithms in Semidefinite Programming," Report 96-42, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands

Clovis C. Gonzaga
"Complexity of predictor-corrector algorithms for LCP based on a large neighborhood of the central path,"

Jacek Gondzio
"Warm Start of the Primal-Dual Method Applied in the Cutting Plane Scheme," Logilab Technical Report 96.3, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4, Switzerland, May 19, 1996. Revised April, 1997.

Lieven Vandenberghe, Stephen Boyd, Shao-Po Wu
"Determinant maximization with linear matrix inequality constraints," Technical Report, Information Systems Laboratory, Stanford University. Submitted to SIMAX, March 1996.

Farid Alizadeh, Jean-Pierre A. Haeberly and Michael L. Overton
"Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results ," New York University Computer Science Dept Report 721, May 1996

Leonid Faybusovich
"Infinite-dimensional semidefinite programming: regularized determinants and self-concordant barriers," University of Notre Dame, May, 1996

Anders Forsgren and Philip E. Gill
"Primal-Dual Interior Methods For Nonconvex Nonlinear Programming," KTH Department of Mathematics Technical Report TRITA-MAT-1996-OS4
and
UCSD Department of Mathematics Technical Report NA-3

Renato Monteiro and Yin Zhang
"A Unified Analysis for a Class of Path-Following Primal-Dual Interior-Point Algorithms for Semidefinite Programming," work in progress.

Z.-Q. Luo and J. Sun
"Cutting Surfaces And Analytic Center: A Polynomial Algorithm For The Convex Feasibility Problem Defined By Self-Concordant Inequalities," working paper, June 1996.

Yinyu Ye
"How partial knowledge helps to solve linear programs," Working Paper, June, 1996.

Renato D. C. Monteiro and Paulo Zanjacomo
"A Note on the Existence of the Alizadeh-Haeberly-Overton Direction for Semidefinite Programming," note. June, 1996.

Abbas Seifi and Levent Tuncel
"A Constant-Potential Infeasible-Start Interior-Point Algorithm with Computational Experiments and Applications," A. Seifi and L. Tuncel, A constant-potential infeasible-start interior-point algorithm with computational experiments and applications, Research Report 96--07, Department of Combinatorics and Optimization, University of Waterloo, Waterloo Ontario, Canada, June 1996.

Jacek Gondzio and Robert Sarkissian
"Column generation with a primal-dual method," Logilab Technical Report 96.6 Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4, Switzerland, June 1996

Rongqin Sheng, Florian A. Potra and Jun Ji
"On a general class of interior-point algorithms for semidefinite programming with polynomial complexity and superlinear convergence," Reports on Computational Mathematics, No. 89/1996, Department of Mathematics, The University of Iowa

R. Byrd, J.C. Gilbert and J. Nocedal
"A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming," Report OTC 96/02 Optimization Technology Center, Northwestern University, Evanston IL 60208 (To appear also as an INRIA report) Iowa

Erling D. Andersen and Yinyu Ye
"A computational study of the homogeneous algorithm for large-scale convex optimization," Publications from Department of Management no. 3/1996, Odense University, Denmark.

Masakazu Muramatsu
"Affine scaling algorithm fails for semidefinite programming," Research report No.16, Department of Mechanical Engineering, Sophia University, July 1996.

Jos F. Sturm and Shuzhong Zhang
"On the Long-Step Path-Following Method for Semidefinite Programming," Report 9638/A, Econometric Institute, Erasmus University Rotterdam, the Netherlands (1996) 9 pages.

Jos F. Sturm and Shuzhong Zhang
"On Weighted Centers for Semidefinite Programming," Report 9636/A, Econometric Institute, Erasmus University Rotterdam, the Netherlands (1996) 19 pages.

Jos F. Sturm and Shuzhong Zhang
"An Interior Point Method, Based on Rank-One Updates, For Linear Programming," Report 9546/A, Econometric Institute, Erasmus University Rotterdam, the Netherlands (1995) 12 pages.

Renato D.C. Monteiro
"Polynomial Convergence of Primal-Dual Algorithms for Semidefinite Programming Based on Monteiro and Zhang Family of Directions," School of ISyE, Georgia Tech, GA 30332 USA. July 1996

D.Haglin, J. Kaliski, C. Roos, T. Terlaky
"LOGARITHMIC BARRIER DECOMPOSITION METHODS FOR SEMI-INFINITE PROGRAMMING," TR-1996-51, Delft University of Technology, P.O.Box 5031, 2600 GA, Delft, The Netherlands

Paul Tseng
"Search Directions and Convergence Analysis of Some Infeasible Path-following Methods for the Monotone Semi-Definite LCP," Report, Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A.

Erling D. Andersen
"On exploiting problem structure in a basis identifications procedure for linear programming," Publications from Department of Management, Odense University, Denmark, no. 6, 1996.

Renato D.C. Monteiro and Takashi Tsuchiya
"Polynomiality of Primal-Dual Algorithms for Semidefinite Linear Complementarity Problems Based on the Kojima-Shindoh-Hara Family of Directions," Report Memorandum No 617 , The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, JAPAN.

Florian A. Potra and Rongqin Sheng
"Superlinear convergence of a predictor-corrector method for semidefinite programming without shrinking central path neighborhood," Reports on Computational Mathematics, No. 91, Department of Mathematics, The University of Iowa, August, 1996.

Anshul Gupta
"Graph partitioning based sparse matrix orderings for interior-point algorithms," IBM Research Report RC 20467, IBM T. J. Watson Research Center, Yorktown Heights, N.Y., May, 1996.

Charles R. Johnson, Brenda Kroschel, and Henry Wolkowicz
"An interior-point method for approximate positive semidefinite completions," University of Waterloo CORR Report 95-11.

MIchael Todd
"On adjusting parameters in homotopy methods for linear programming," Technical Report No. 1170, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801.

Minyue Fu, Zhi-Quan Luo and Yinyu Ye
" Approximation algorithms for quadratic programming," Manuscript, Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, CANADA L8S 4K1

Stefan E. Karisch, Franz Rendl, Henry Wolkowicz, and Qing Zhao
"Semidefinite Programming Relaxations for the Quadratic Assignment Problem," CORR Report 95/27, University of Waterloo, September, 1996.

Robert M. Freund and Shinji Mizuno
"Interior Point Methods: Current Status and Future Directions," To appear in Optima as a feature article, Volume 51, 1996.

Song Xu and Jim Burke
"A Polynomial Time Interior- Point Path Following Agorithm for LCP Based on Chen-Harker-Kanzow Smoothing Techniques," Preprint, September 1996, Mathematics Department, University of Washington, Seattle, WA 98195-4350.

Henry Wolkowicz and Qing Zhao
"Semidefinite Programming Relaxations for the Graph Partitioning Problem," preprint, Department of Combinatorics and Optimization, University of Waterloo, October, 1996.

Jos F. Sturm
"Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution exists," Report 9656/A, Econometric Institute, Erasmus University Rotterdam, September, 1996.

Harvey J. Greenberg
"Rim sensitivity analysis from an interior solution," Report Number CCM 86, Center for Computational Mathematics, Mathematics Department, University of Colorado at Denver, Denver, October, 1996.

Katsuki Fujisawa, Masakazu Kojima and Kazuhide Nakata
SDPA (Semidefinite Programming Algorithm) Annoucement, October, 1996.

Levent Tuncel
"Primal-dual symmetry and scale invariance of interior-point algorithms for convex optimization," Research Report 96--18, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, November 1996.

Renato D.C. Monteiro and Takashi T. Tsuchiya
"Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming," Report Memorandum No. 627, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, JAPAN.

Gongyun Zhao
"Interior Point Methods With Decomposition For Linear Programs," Research Report No. 686, Department of Mathematics, National University of Singapore, Singapore, 1996.

H.J. Greenberg and A.G. Holder and C. Roos and T. Terlaky
"On the Dimension of the Set of Rim Perturbations for Optimal Partition Invariance," Technical Report CCM No. 94, Center for Computational Mathematics, Mathematics Department, University of Colorado at Denver, Denver, CO 80217-3364.

F. Sharifi Mokhtarian and J.-L. Goffin
"A Nonlinear Analytic Center Cutting Plane Method for a Class of Convex Programming Problems," GERAD Technical Report G-96-53, November, 1996.

K.C. Toh, M.J. Todd, and R.H. Tutuncu
"SDPT3 --- a Matlab software package for semidefinite programming," manuscript.

Christoph Helmberg
"Fixing Variables in Semidefinite Relaxations," Preprint SC-96-43, December 1996, Konrad Zuse Zentrum fer Informationstechnik Berlin, Takustrasse 7, D-14195 Berlin-Dahlem, Germany.

Gongyun Zhao
"Interior point algorithms for linear complementarity problems based on large neighborhoods of the central path," Research Report No. 650, Dept of Mathematics, National University of Singapore, Singapore.

E. de Klerk, C. Roos, T. Terlaky
"On primal-dual pa th following algorithms for semidefinite programming.," Report 96-102, Reports of the Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands.

J. Castro and N. Nabona
"Primal-Dual interior point method for multicommodity network flows with side constraints and comparison with alternative methods," Manuscript, December, 1996.

Keisuke Hotta and Akiko Yoshise
"Global convergence of a class of non-interior-point algorithms using Chen-Harker-Kanzow functions for nonlinear complementarity problems," Discussion Paper Series No. 708, Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba, Ibaraki 305, Japan, December, 1996.

Kurt M. Anstreicher
"Towards a Practical Volumetric Cutting Plane Method for Convex Programming," Technical Report, January 17, 1997.

Jun Ji, Florian A. Potra and Rongqin Sheng
"On the local convergence of a predictor-corrector method for semidefinite programming," Reports on Computational Mathematics, No. 98/1997, Department of Mathematics, The University of Iowa.

Jim Burke and Song Xu
"The global linear convergence of a non-interior path-following algorithm for linear complementarity problems," Technical report, Department of Mathematics, University of Washington, Seattle, WA 98195, December 1996.

Stephen Vavasis and Yinyu Ye
"A simplification to A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix," Technical Note, Department of Management Science, University of Iowa, Iowa City, January 1997.

Song Xu
"The Global Linear Convergence of an Infeasible Non-Interior Path-Following Algorithm for Complementarity Problems with Uniform P-Functions," Technical Report, Department of Mathematics, University of Washington, Seattle, WA 98195, December, 1996.

L. Mosheyev and M. Zibulevsky
"Penalty/Barrier Multiplier Algorithm for Semidefinite Programming: Dual Bounds and Implementation," Research Report #1/96, Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology .

L.Faybusovich
"Linear systems in Jordan algebras and primal-dual interior-point algorithms," Technical Report, University of Notre Dame, August, 1996

Katsuki Fujisawa, Masakazu Kojima and Kazuhide Nakata
"Exploiting Sparsity in Primal-Dual Interior-Point Methods for Semidefinite Programming," Research Report on Mathematical and Computing Sciences B-324, Tokyo Institute of Technology, January, 1997

E. Bobrovnikova and S. Vavasis
"Accurate solution of weighted least squares by iterative methods," Argonne National Laboratory Preprint ANL/MCS-P644-0297, February, 1997.

Josef Stoer, Martin Wechs, and Shinji Mizuno
"High order infeasible-interior-point methods for solving sufficient linear complementarity problems," Research Memorandum 634, The Institute of Statistical Mathematics, Tokyo, Japan, February, 1997.

John E. Mitchell
"Computational experience with an interior point cutting plane algorithm," Math Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, February, 1997. Revised April, 1997.

E. Bai, Y. Ye and R. Tempo
"Bounded Error Parameter Estimation: A Sequential Analytic Center Approach," Working Paper, Dept. of Management Science, University of Iowa, IA, 52242, USA.

Marina Epelman and Robert M. Freund
"Condition Number Complexity of an Elementary Algorithm for Resolving a Conic Linear System," Technical Report, February, 1997.

Renato D.C. Monteiro and Jong-Shi Pang
"A Potential Reduction Newton Method for Constrained Equations," working paper, School of ISyE, Georgia Tech, USA, March 1997.

Ming Gu
"On Primal-Dual Interior Point Methods for Semidefinite Programming," CAM report 97-12, Department of Mathematics, University of California, Los Angeles, Calif., March, 1997.

Brian Borchers
"CSDP, a C library for semidefinite programming," March, 1997.

E. de Klerk, C. Roos, T. Terlaky
"Infeasible start, semidefinite programming algorithms via self-dual embeddings," Report 97-10, Reports of the Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands.

Gongyun Zhao and Jie Sun
"On the rate of local convergence of high-order infeasible-path-following algorithms for $P_*$-LCP with or without strictly complementary solutions," Research Report No. 698, Department of Mathematics, National University of Singapore, March, 1997.

F. Alizadeh, J.-P. Haeberly, M. V. Nayakkankuppam and M. L. Overton
"SDPpack User's Guide, Version 0.8 BETA," NYU Computer Science Department Technical Report 734, March 1997.

Stephen Portnoy and Roger Koenker
" The Gaussian Hare and the Laplacian Tortoise: Computability of squared-error vs. absolute-error estimators," Department of Statistics, University of Illinois Urbana-Champaign, March, 1997.

Yinyu Ye
"Approximating quadratic programming with bound constraints," Working Paper, Department of Management Science, The University of Iowa, Iowa City, March 1997.

Kurt M. Anstreicher
"Ellipsoidal Approximations of Convex Sets Based on the Volumetric Barrier," Technical Report, March, 1997.

Masakazu Kojima, Masayuki Shida and Susumu Shindoh
"Search Directions in the SDP and the Monotone SDLCP: Generalization and Inexact Computation," Research Report B-327, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 157, Japan, March 1997.

M. Muramatsu and R. J. Vanderbei
"Primal-dual affine-scaling algorithms fail for semidefinite programming," Technical Report SOR 97-05, Princeton University, NJ 08544, April, 1997 (revised June, 1997)

Terrence K. Kelly and Joseph G. Ecker
"EPM: An Exterior Point Method for Linear Programming," April, 1997

E. D. Andersen and K. D. Andersen
"The APOS linear programming solver: an implementation of the homogeneous algorithm," CORE, Universite Catholique de Louvain, CORE discussion paper #9337, 1997.

Yinyu Ye
"Approximating quadratic programming with quadratic constraints," Working Paper, Department of Management Science, The University of Iowa, Iowa City, IA 52242, April, 1997.

Margaret H. Wright
"Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming," Technical Report 97-4-04, Computing Sciences Research Bell Laboratories, Murray Hill, New Jersey April 25, 1997.

H.J. Greenberg
"Matrix Sensitivity Analysis from an Interior Solution of a Linear Program," Center for Computational Mathematics, Mathematics Department, University of Colorado at Denver, 1997.

Florian A. Potra, Rongqin Sheng, and Nathan Brixius
"SDPHA: A MATLAB implementation of homogeneous interior-point algorithms for semidefinite programming," Reports on Computational Mathematics, No. 100/1997, Department of Mathematics, The University of Iowa, April, 1997.

Stephen G. Nash and Ariela Sofer
"On the Complexity of a Practical Interior-Point Method," to appear in SIAM Journal on Optimization, 1997.

Csaba Meszaros
"On free variables in interior point methods," Technical Report DOC 97/4, Imperial College, London, UK, June, 1997.

J. Gondzio and J.-P. Vial
"Warm start and epsilon-subgradients in the cutting plane scheme for block-angular linear programs," Logilab Technical Report 97.1, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4, Switzerland, June 1997.

Z.-Q. Luo, J.F. Sturm and S. Zhang
"Duality results for conic convex programming," Report 9719/A, Econometric Institute EUR, The Netherlands, April 1997.

E. Fragniere, J. Gondzio, R. Sarkissian and J.-P. Vial
"Structure exploiting tool in algebraic modeling languages," Logilab Technical Report 97.2, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4, Switzerland, June, 1997.

J. Peña
"Understanding the geometry of infeasible perturbations of a conic linear system," Manuscript, Computational and Applied Mathematics Program, Cornell University, June, 1997.

J. Peña and J. Renegar
"Quickly computing backward-approximate solutions for ill-conditioned systems of linear inequalities and forward-approximate solutions for well-conditioned systems," Manuscript, Computational and Applied Mathematics Program, Cornell University, June, 1997.

Stefan E. Karisch, Franz Rendl, and Jens Clausen
"Solving graph bisection problems with semidefinite programming," Technical Report DIKU-TR-97/9, Department of Computer Science, University of Copenhagen, July 1997.

Renato D.C. Monteiro and Paulo R. Zanjacomo
"Implementation of Primal-Dual Methods for Semidefinite Programming Based on Monteiro and Tsuchiya Newton Directions and their Variants," manuscript, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, July 1997. Revised August, 1997.

Y. Nesterov and J.-Ph. Vial
"Homogeneous Analytic Center Cutting Plane Methods for Convex Problems and Variational Inequalities," Logilab Technical Report 1997.4, July 9, 1997.

Thomas F. Coleman, Joseph Czyzyk, Chunguang Sun, Michael Wagner, Stephen J. Wright
"pPCx: Parallel software for linear programming," CCOP TR 96-14, Cornell University, Ithaca, NY 14853, December, 1996.

K.C. Toh
"Search directions for primal-dual interior point methods in semidefinite programming," Technical Report, Department of Mathematics, National University of Singapore, Singapore, July, 1997.

John Mitchell
"An interior point cutting plane algorithm for Ising spin glass problems," Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, July 15, 1997.

Abdo Y. Alfakih and Amir Khandani and Henry Wolkowicz
"An interior-point algorithms for the Euclidean distance matrix completion problem," Research Report CORR 97-9, University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario N2L 3G1, Canada.

Detong Zhang and Yin Zhang
"On Constructing Interior-Point Path-Following Methods for Certain Semimonotone Linear Complementarity Problems," TR97-19, CAAM, Rice University, July 1997.

Richard Byrd, Mary Beth Hribar, and Jorge Nocedal
"An Interior Point Algorithm for Large Scale Nonlinear Programming," OTC Technical Report 97/05, Optimization Technology Center, July, 1997.

J.F. Sturm,
"Primal-Dual Interior Point Approach to Semidefinite Programming," Ph.D. Thesis, Tinbergen Institute Research Series vol. 156, Thesis Publishers, Amsterdam, The Netherlands, 1997.

S. J. Wright,
"On the convergence of the Newton/log-barrier method," Preprint ANL.MCS-P681-0897, MCS Division, Argonne National Laboratory, August, 1997.
Yinyu Ye
"Approximating quadratic optimization with linear and boolean constraints," Working Paper, Department of Management Sciences, The University of Iowa, IA, USA, August, 1997

Jean-Louis Goffin and Jean-Philippe Vial
"A two-cut approach in the analytic center cutting plane method," Logilab Technical Report 97.6, Logilab, Department of Management Studies University of Geneva, August, 1997.

Christoph Helmberg and Franz Rendl
"A Spectral Bundle Method for Semidefinite Programming," ZIB Preprint SC 97-37, August 1997, revised October 1997, Konrad-Zuse-Zentrum fuer Informationstechnik Berlin, Takustrasse 7, D-14195 Berlin, Germany.

L. Biegler, J. Nocedal, C. Schmid and D. Ternet
"Numerical Experience with a Reduced Hessian Method for Large Scale Optimization," Report OTC 97/06 Optimization Technology Center, July 1997.

"On self-concordant convex-concave functions," Research report #3/97, June 1977, Optimization Laboratory Faculty of Industrial Engineering and Management at Technion, Technion City, Haifa 32000, Israel.

A. Ben-Tal and A. Nemirovski
"Structural design via Semidefinite Programming," Working paper, August 1997, Optimization Laboratory, Faculty of Industrial Engineering and Management at Technion, Technion City, Haifa 32000, Israel.

A. Nemirovski
"On normal self-concordant barriers and long-step interior point methods," Working paper, August 1997, Optimization Laboratory, Faculty of Industrial Engineering and Management at Technion, Technion City, Haifa 32000, Israel.

Guoliang Xue and Yinyu Ye
"An Efficient Algorithm for Minimizing a Sum of P-Norms," Working Paper, Department of Computer Science, The University of Vermont, Burlington, VT 05405-0156.

L.Faybusovich
"Euclidean Jordan algebras and Interior-point algorithms," Report, June 1997.

Csaba Meszaros
"Steplengths in infeasible primal-dual interior point algorithms of convex quadratic programming," Departmental Technical Report DOC 97/7, Imperial College, London, UK, July, 1997.

Steven Benson, Yinyu Ye, and Xiong Zhang
"Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization (Revision)," Working Paper, Department of Management Science, University of Iowa, IA, 52242, USA.

Paul Tseng
"Analysis of an Infeasible Interior Path -Following Method for Complementarity Problems," Report, Department of Mathematics, University of Washington, Seattle, August 1997 (revised September 1997).

John Mitchell and Brian Borchers
"Solving linear ordering problems with a combined interior point/simplex cutting plane algorithm," Mathematical Sciences, RPI, Troy NY 12180 USA, September 1997.

A.J. Quist, E. de Klerk, C. Roos, T. Terlaky
"Copositive Relaxation for General Quadratic Programming," Optimization Group TU Delft, Faculty of Information Technology and Systems, Delft University of Technology. To appear in Optimization Methods and Software.

Rongqin Sheng and Florian A. Potra
"Nonsymmetric Search Directions for Semidefinite Programming," Preprint ANL/MCS-P692-0997, Mathematics and Computer Science Division, Argonne National Laboratory, September 1997.

Robert M. Freund and Jorge Vera
"Condition-Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm," MIT Operations Research Center Technical Report, September, 1997.

Eva K. Lee and John E. Mitchell
"Computational Experience of an Interior-Point SQP Algorithm in a Parallel Branch-and-Bound Framework," Technical Report LEC 97-08, Industrial and Systems Engineering, Georgia Institute of Technology.

Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima and Kazuhide Nakata
"Numerical Evaluation of SDPA (SemiDefinite Programming Algorithm)," Research Report B-330, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152, September 1997.

Michael Todd
"On search directions in interior-point methods for semidefinite programming," Technical Report No. 1205, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801, October, 1997.

Takashi Tsuchiya
"A polynomial primal-dual path-following algorithm for second-order cone programming," Research Memorandum No. 649, The Institute of Statistical Mathematics, Tokyo 106 JAPAN, October, 1997

Roland W. Freund, Florian Jarre, Shinji Mizuno
"Convergence of a Class of Inexact Interior-Point Algorithms for Linear Programs," Numerical Analysis Manuscript 97--3--11, Bell Laboratories, Murray Hill, New Jersey.

T. Illés, C. Roos and T. Terlaky
"Polynomial Affine -Scaling Algorithms for $P_*(\kappa)$ Linear Complementarity Problems," Reports of the Faculty of Technical Mathematics and Informatics Nr. 97-21, Delft University of Technology, Delft, March, 1997

Florian Jarre, Martin Wechs
"Extending Mehrotra's Corrector for Linear Programs," Preprint Nr. 219, Mathematische Institute der Universitaet Wuerzburg Dec. 1996, revised Oct. 1997

A. Iusem and R.D.C. Monteiro
"On Dual Convergence of the Generalized Proximal Point Method with Bregman Distances," manuscript, School of ISyE, Georgia Tech, Atlanta, GA 30332, October 1997.

J. Peña
"Computing the distance to infeasibility: theoretical and practical issues," technical report, Center for Applied Mathematics, Cornell University, October, 1997.

G. Pataki and L. Tuncel
"On the generic properties of convex optimization problems in conic form," Research Report 97-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, September 1997.

T. Stephen and L. Tuncel
"On a representation of the matching polytope via semidefinite liftings," Research Report 97-11, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, July 1997.

A. R. L. Oliveira and D. C. Sorensen
"A New Class of Preconditioners for Large-Scale Linear Systems from Interior Point Methods for Linear Programming," Technical Report TR97-27, Department of Computational and Applied Mathematics, Rice University, Houston TX, November 1997.

A. R. L. Oliveira and D. C. Sorensen
"Computational Experience with a Preconditioner for Interior Point Methods for Linear Programming," Technical Report TR97-28, Department of Computational and Applied Mathematics, Rice University, Houston TX, November 1997.

"Optimization with Semidefinite, Quadratic and Linear Constraints," RUTCOR, RRR Report 23-97, November 1997.

Ioannis Akrotirianakis and Berc Rustem
"A Globally Convergent Interior Point Algorithm for General Non-Linear Programming Problems," Technical Report 97/14, (November 1997), Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, London SW7 2BZ, UK.

Levent Tuncel
"On the condition numbers for polyhedra in Karmarkar's form," Research Report CORR 97-24, November 1997.

David M. Gay, Michael L. Overton, Margaret H. Wright
"A Primal-Dual Interior Method for Nonconvex Nonlinear Programming," Technical report 97-4-08, Computing Sciences Research, Bell Labs, Murray Hill, NJ, July 29, 1997

Kurt M. Anstreicher
"The Volumetric Barrier for Semidefinite Programming," Technical Report, January, 1998.

Jacek Gondzio, Robert Sarkissian and Jean-Philippe Vial
"Parallel implementation of a central decomposition method for solving large scale planning problems," HEC Technical Report 98.1, Section of Management Studies, University of Geneva, January, 1998.

R. Byrd, G. Liu and J. Nocedal
"On the Local Behavior of an Interior Point Method for Nonlinear Programming," Report OTC 98/02, Optimization Technology Center, January, 1998. (To appear in the Proceedings of the 1997 Dundee Conference on Numerical Analysis)

Erling D. Andersen and Knud D. Andersen
"A parallel interior-point algorithm for linear programming on a shared memory machine," CORE Discussion Paper 9808, CORE, Louvain-La-Neuve, Belgium, 1998.

S. J. Wright
"Effects of finite-precision arithmetic on interior-point methods for nonlinear programming," Preprint ANL/MCS-P705-0198, MCS Division, Argonne National Laboratory, January, 1998.

Peter Kas, Emil Klafszky, Levente Malyusz, Goekhan Izbirak
"Minimization of Bregman's divergence functions, and its relation to linear programming," Department of Building Management and Organization, Technical University of Budapest Muegyetem rkp.3., Budapest, 1111 Hungary.

Chih-Jen Lin and Romesh Saigal
"On Solving Large-Scale Semidefinite Programming Problems: A Case Study of Quadratic Assignment Problem," Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, December 1997

S. Benson, Y. Ye and X. Zhang
"Mixed Linear and Semidefinite P rogramming for Combinatorial and Quadratic Optimization," Working Paper, Applied Mathematics and Computational Sciences, University of Iowa, Iowa City, IA 52242, February, 1998.

Nesterov Yu., O. Peton, J.-Ph Vial
"Homogeneous An alytic Center Cutting Plane Methods with Approximate Centers," HEC Technical Report 98.3, Department of Management Studies, University of Geneva, Switzerland, February 1998.

L. Faybusovich
"Euclidean Jordan algebras and generalized affine-scaling vector fields," Research report, University of Notre Dame, January, 1998

Hans-Jakob L\"uthi, Benno B\"ueler
"The Analytic Center Quadratic Cut Method (ACQCM) for Strongly Monotone Variational Inequality Problems," Institute for Operations Research, ETH Zurich March 1998

Masakazu Kojima and Levent Tuncel
"Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets," Research Report B-338, Dept. of Mathematical Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguoro, Tokyo 152, March 1998

Anna Altman and Jacek Gondzio
"Regularized Symmet ric Indefinite Systems in Interior Point Methods for Linear and Quadratic Optimization," Logilab Technical Report 98.6, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4, Switzerland, March 1998.

Cs. Meszaros
"On a property of the Cholesky factorization and its consequences in interior point methods," WP 98-7 Laboratory of Operations Research and Decision Systems Hungarian Academy of Sciences

Renato Monteiro and Paulo Zanjacomo
"General Interior-Point Maps and Existence of Weighted Paths for Nonlinear Semidefinite Complementarity Problems," Technical Report, School of ISyE, Georgia Tech, April 1998.

Csaba Meszaros
"The separable and non-separable formulations of convex quadratic problems in interior point methods ," WP 98-3 Laboratory of Operations Research and Decision Systems Hungarian Academy of Sciences, April, 1998

Asic, M.D., Kovacevic-Vujcic, V.V.
"Ill-Conditioned ness and Interior-Point Methods," Technical Report, Laboratory for OR, February 1998, Faculty of Organizational Sciences, University of Belgrade, Jove Ilica 154, 11040 Belgrade, Yugoslavia

Anders Forsgren
"Optimality conditions for nonconve x semidefinite programming," Technical Report TRITA-MAT-1998-OS6, Department of Mathematics, Royal Institute of Technology (KTH) SE-100 44 Stockholm, Sweden May 1998

Csaba Meszaros
"On the sparsity issues of interior point methods for quadratic programming," WP 98-4 Laboratory of Operations Research and Decision Systems, Hungarian Academy of Sciences

Serge Kruk, Masakazu Muramatsu, Franz Rendl, Robert J. Vanderbei, Henry Wolkowicz
"The Gauss-Newton Direction in Semidefinite Programming," Manuscript, May, 1998.

Kurt M. Anstreicher
"On the Equivalence of Convex Programming Bounds for Boolean Quadratic Programming," Technical Report, May, 1998.

L. Faybusovich
"A Jordan-algebraic approach to potential-reduction algorithms," Research report, Department of Mathematics, University of Notre Dame, April, 1998

Francisco Facchinei, Andreas Fischer, Christian Kanzow
"On the Identification of Zero Variables in an Interior-Point Framework," Mathematical Programming Technical Report 98-06, Computer Sciences Department, University of Wisconsin, Madison, WI, May 1998.

Kurt Anstreicher and Henry Wolkowicz
"On Lagrangian Relaxation of Quadratic Matrix Constraints," Research Report CORR 98-24 University of Waterloo Department of Combinatorics and Optimization Waterloo, Ontario N2L 3G1, Canada

Renato D.C. Monteiro and Takashi Tsuchiya
"Polynomial Convergence of Primal-Dual Algorithms for the Second-Order Cone Program Based on the MZ-Family of Directions," manuscript, May 1998, School of ISyE, Georgia Tech, Atlanta, GA, 30338.

Masakazu Kojima and Levent Tuncel
"Monotonicity of primal-dual interior-point algorithms for semidefinite programming problems," Research Report 98-23, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, May 1998. Also: Technical Report B-340, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan, May 1998.

"Associative Algebras, Symmetric Cones and Polynomial Time Interior Point Algorithms," Report number RRR 17-98, RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway NJ 08854-8003.

Jean-Louis Goffin and Jean-Philippe Vial
"Multiple cuts in the analytic center cutting plane method," Logilab Technical Report 98.10, Department of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4 Switzerland, June, 1998.

Takashi Tsuchiya
"A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming ," Research Memorandum No. 664, The Institute of Statistical Mathematics, Tokyo, Japan

Brian Borchers
"CSDP, A C library for semidefinite programming."

Stephen Wright
"Modified Cholesky Factorizations in Interior-Point Algorithms for Linear Programming," Preprint ANL/MCS-P600-0596, Mathematics and Computer Science Division, Argonne National Laboratory, May, 1996. Revised June, 1998.

Arkadi Nemirovski, Kees Roos, Tam\'as Terlaky
"On Maximization of Quadratic form over Intersection of Ellipsoids with Common Center," Report No. 98-??, Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.

E. Fragniere, J. Gondzio and J.-P. Vial
"Building and Solving Large-scale Stochastic Programs on an Affordable Distributed Computing System," Logilab Technical Report 98.11, Department of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4 Switzerland, June, 1998. Revised March, 1999.

Robert J. Vanderbei and David. F. Shanno
"An Interior--Point Algorithm for Nonconvex Nonlinear Programming," SOR 97-21, Princeton University, May 1998 (REVISED)

Gongyun Zhao
"Barrier function in the Lagrangian dual method for solving multi-stage stochastic nonlinear programs," Working paper, Dept of Math., National University of Singapore, Singapore, 1998.

Gongyun Zhao
"Log-barrier decomposition methods for solving two-stage stochastic programs," Working paper, Dept of Math., National University of Singapore, Singapore, 1998. (revised)

Margaret H. Wright
"The Interior-Point Revolution in Constrained Optimization," Technical Report 98-4-09, Computing Sciences Research Center, Bell Labs, Murray Hill, New Jersey 07974

Brian Borchers
"SDPLIB 1.0, a collection of semidefinite programming test problems," July 3, 1998.

Jordi Castro
"A specialized interior point algorithm for multicommodity flows," Manuscript, July 1998, Statistics and Operations Research, Universitat Rovira i Virgili, 43006 Tarragona (Spain).

Thomas Urban, Andre Tits and Craigl Lawrence
"A Primal-Dual Interior-Point Method for Nonconvex Optimization with Multiple Logarithmic Barrier Parameters and with Strong Convergence Properties," Institute for Systems Research Technical Report TR 98-27, University of Maryland,College Park.

Kurt Anstreicher, Xin Chen, Henry Wolkowicz, Ya-Xiang Yuan
"Strong Duality for a Trust-Region Type Relaxation of the Quadratic Assignment Problem," Research Report CORR 98-31, University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario N2L 3G1, Canada.

Yinyu Ye
"Approximating global quadratic optimization with convex quadratic constraints ," Working Paper, Department of Management Sciences, The University of Iowa, Iowa City, Iowa 52242, U.S.A.

T. Terlaky
"An Easy Way to Teach Interior Point Methods," Report 98-24, Faculty of Information Technology and Systems Subfaculty of Technical Mathematics and Informatics, Department of Statistics, Stochastic and Operations Research Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.

T. Illés, J. Peng, C. Roos and T. Terlaky
"A Strongly Polynomial Rounding Procedure Yielding A Maximally Complementary Solution for $P_*(\kappa)$ Linear Complementarity Problems ," Report 98-15, Faculty of Information Technology and Systems Subfaculty of Technical Mathematics and Informatics, Department of Statistics, Stochastic and Operations Research Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.

J. Peng, C. Roos and T. Terlaky
"New Complexity Analysis of the Primal-Dual Newton Method for Linear Optimization," Technical Report 98-05, Delft University of Technology, Faculty of Technical Mathematics and Informatics, P.O. Box 5031, 2600 GA Delft, The Netherlands.

Masakazu Kojima and Levent Tuncel
"Discretization and Localization in Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems," Research Report B-341, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguoro, Tokyo 152, July, 1998. Also issued as COOR 98-34, Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

Shinji Mizuno and Michael J. Todd
"On two homogeneous self-dual systems for linear programming and its extensions," Research Memorandum 687, The Institute of Statistical Mathematics, Tokyo, Japan. Also issued as Technical Report No. 1213, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY.

F. Jarre
"A QQP-Minimization Method for Semidefinite and Smooth Nonconvex Programs ," Report, Universitaet Trier, August 1998.

Jos F. Sturm
"Error bounds for linear matrix inequalities," Comunications Research Lab., McMaster University, 1280 Main Street West, HAMILTON , ONTARIO L8S 4K1, CANADA, May 1998.

Jos F. Sturm
"Similarity and other spectral relations for symmetric cones," Communications Research Lab., McMaster University, 1280 Main Street West, HAMILTON , ONTARIO L8S 4K1, CANADA, July 1998

Jos F. Sturm
"Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Communications Research Lab, McMaster University, Hamilton, Ontario, Canada. August 1998.

Knud D. Andersen, Edmund Christiansen, Andrew R. Conn and Michael L. Overton
"An Efficient Primal-Dual Interior-Point Method for Minimizing a Sum of Euclidean Norms," August, 1998.

Stephen G. Nash and Ariela Sofer
"Why Extrapolation Helps Barrier Methods," September, 1998.

M.J. Todd, Levent Tuncel and Yinyu Ye
"Probabilistic analysis of two complexity measures for linear programming problems," TR 1219, School of Operations Research and Industrial Engineering, Cornell University, Ithaca NY, USA. Also: CORR 98-48, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, October 1998.

Manuel A. Nunez
"A Characterization of Ill-Posed Data Instances for Convex Programming," School of Business and Economics, Chapman University, 333 N Glassell St., Orange, CA 92866, September 10, 1998.

Paul Armand, J. Charles Gilbert, Sophie Jan-J\'egou
"A Feasible BFGS Interior Point Algorithm for Solving Strongly Convex Minimization Problems," Research Report 3500, INRIA, France, October, 1998.

Kurt M. Anstreicher
"The Volumetric Barrier for Convex Quadratic Constraints," Dept. of Management Sciences, University of Iowa, Iowa City, October 1998.

Jean-Pierre Haeberly, Madhu Nayakkankuppam, and Michael Overton
"Extending Mehrotra and Gondzio Higher Order Methods to Mixed Semidefinite-Quadratic-Linear Programming," To appear in Optimization Methods and Software.

D. Cvetkovic, M. Cangalovic, V. Kovacevic-Vujcic
"Semidefini te relaxations of traveling salesman problem," Technical Report 902-98, Laboratory for Operations Research, Faculty of Organizational Sciences, University of Belgrade, November 1998

"On polyhedral approximations of the second-order cone," Research Report #3/98, Optimization Laboratory, Faculty of Indistrial Angineering and Management, Technion -- Israel Institute of Technology, Technion City, Haifa 32000, Israel

"On the quality of SDP approximations of uncertain SDP programs," Research Report #4/98, Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel

Levent Tuncel
"Approximating the complexity measure of Vavasis-Ye algorithm is NP-hard," Research Report CORR 98-51, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada, November 1998.

Marina Epelman and Robert M. Freund
"Condition Number Complexity of an Elementary Algorithm for Computing a Reliable Solution of a Conic Linear System," Massachusetts Institute of Technology, December 1998

Sam Burer and Renato D.C. Monteiro
"An Efficient Algorithm for Solving the MAXCUT SDP Relaxation," Manuscript, School of ISyE, Georgia Tech, Atlanta, GA 30332, USA, December, 1998.

Keisuke Hotta, Masatora Inaba and Akiko Yoshise
"A complexity analysis of a smoothing method using CHKS-functions for monotone linear complementarity problems," Discussion Paper Series No. 807, Institute of Policy and Planning Sciences, Univ ersity of Tsukuba, Tsukuba, Ibaraki 305, Japan.

Robert J. Vanderbei and Hande Yurttan
"Using LOQO to Solve Second-Order Cone Programming Problems," Tech Report SOR-98-9, Princeton University, Princeton NJ 08544

Kurt Anstreicher
"Eigenvalue bounds versus semidefinite relaxations for the quadratic assignment problem," Dept. of Management Sciences, University of Iowa, February 1999

K. Fukuda and T. Terlaky
"On the existence of a short admissible pivot sequences for feasibility and linear optimization problems," Techinal Report, January 1999, Faculty of ITS/TWI, Delft University of Technology, Delft, The Netherlands

J. Peng, C. Roos and T. Terlaky
"New Complexity Analysis of the Primal-Dual Method for Semidefinite Optimization based on the NT-direction ," Techinal Report, January 1999, Faculty of ITS/TWI, Delft University of Technology, Delft, The Netherlands

E. de Klerk, J. Peng, C. Roos, and T. Terlaky
"A scaled Gauss-Newton Primal-Dual Search Direction for Semidefinite Optimization," Report of the Faculty ITS/TWI, Delft University of Technology, Delft, The Netherlands, 1999.

Masakazu Kojima
"Moderate Nonlinearity = Convexity + Quadratic Concavity," Research Report B-348, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8852, Japan, March 1999

Akiko Takeda, Yang Dai, Mituhiro Fukuda, and Masakazu Kojima
"Towards the Implementation of Successive Convex Relaxation Method for Nonconvex Quadratic Optimization Problems," Research Reports on Information Sciences, No. B-347, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, March 1999.

Yinyu Ye
"A .699-Approximation Algorithm for Max-Bisection," Working Note, Department of Management Sciences, Henry B. Tippie College of Business, The University of Iowa, Iowa City, Iowa 52242.

Jean-Louis Goffin and Jean-Philippe Vial
"Convex nondifferentiable optimization: a survey focussed on the analytic center cutting plane method," Logilab Technical Report 99.02, Department of Management Studies, University of Geneva, Switzerland, February, 1999.

Florian Jarre
"Comparing two Interior-Point Approaches for Semi-Infinite Programs," Technical Report, Institut fuer Angewandte Mathematik, Universitaet Wuerzburg, Am Hubland, March 1999.

Masakazu Kojima and Akiko Takeda
"Complexity Analysis of Conceptual Successive Convex Relaxation of Nonconvex Set," Research Report B-350, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152, April 1999.

Arjan Berkelaar, Cees Dert, Bart Oldenkamp, Shuzhong Zhang
"A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming," Econometric Institute Report EI-9918/A, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, April, 1999.

David D. Yao, Shuzhong Zhang, Xun Yu Zhou
"LQ Control without Riccati Equations: Stochastic Systems," Econometric Institute Report EI9920/A, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, April, 1999.

Jacek Gondzio and Roy Kouwenberg
"High Performance Computing for Asset Liability Management," Technical Report MS-99-004, Department of Mathematics and Statistics, The University of Edinburgh, Scotland. May 21, 1999.

Levent Tuncel and Song Xu
"On homogeneous convex cones, Caratheodory number, and duality mapping," CORR 99-21, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada, June 1999.

John E. Mitchell
"Restarting after branching in the SDP approach to MAX-CUT and similar combinatorial optimization problem," Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180. June 25, 1999.

G. Gruber, F. Rendl
"Semidefinite Programs whithout feasible interior points," Technical Report, University of Klagenfurt, July, 1999.

Venansius Baryamureeba, Trond Steihaug and Yin Zhang
"Properties of a class of preconditioners for weighted least squares problems," Technical Report No. 170, Department of Informatics, University of Bergen, N-5020 Bergen, Norway and Technical Report No. TR99-16, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, USA. April 30, 1999 (Revised July 6, 1999)

E. D. Andersen, J.E. Mitchell, C. Roos, and T. Terlaky
"A homogenized cutting plane method to solve the convex feasibility problem," ITS/TWI/SSOR, TU Delft, Delft, The Netherlands, and Math Sciences, Rensselaer Polytechnic Institute, Troy NY, August 1998, revised July 1999.

Roland W. Freund, Florian Jarre
"Solving the Sum-of-Ratios Problem by an Interior-Point Method," Numerical Analysis Manuscript 99 3 13, Bell Laboratories, Murray Hill, New Jersey, June 1999.

C. Lemarechal and F. Oustry
"Semidefinite relaxations and Lagrangian duality with application to combinatorial optimization ," RR-3710, INRIA Rhone-Alpes ZIRST - 655 avenue de l'Europe F-38330 Montbonnot Saint-Martin, June 1999

A. R. Conn, N. I. M. Gould, D. Orban, and Ph. L. Toint
"A Primal-Dual Trust-Region Algorithm for Minimizing a Non-convex Function Subject to General Inequality and Linear Equality Constraints," Technical Report RAL-TR-1999-054 Rutherford Appleton Laboratory Chilton, Oxfordshire, England.

Francois Oustry
"A Second-Order Bundle Method to Minimize the Maximum Eigenvalue Function," RR-3738, INRIA Rhone-Alpes ZIRST, 655 avenue de l'Europe F-38330 Montbonnot Saint-Martin, July 1999.

S. J. Wright and D. Orban
"Properties of the log-barrier function on degenerate nonlinear programs," Preprint ANL/MCS-P772-0799, July, 1999.

Samuel Burer and Renato D. C. Monteiro
"A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semidefinite Programming," School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332, August 1999.

Manuel A. Nunez and Robert M. Freund
"Condition-Measure Bounds on the Behavior of the Central Trajectory of a Semi-Definite Program," School of Business and Economics, Chapman University, One University Drive, Orange, CA 92866, and MIT Sloan School of Management, 50 Memorial Drive, Cambridge, MA 02142-1347, August, 1999.

Levent Tuncel
"Generalization of primal-dual interior-point methods to convex optimization problems in conic form," Research Report CORR 99-35, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, August 25, 1999.

M.C. Villalobos, R.A. Tapia, Y. Zhang
"The Behavior of Newton-type Methods on Two Equivalent Systems from Linear Programming," TR9802 (also report CRPC-TR98770-S) Rice University, Computational and Applied Mathematics, Houston, TX September 1998.

Masakazu Kojima and Levent Tuncel
"On the Finite Convergence of Successive SDP Relaxation Methods," Research Report B-354, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan, August 1999. Also issued as Research Report CORR 99-36, Department of Combinatorics and Optimization, University of Waterloo, Ontario, Canada

R. J. Caron, H. J. Greenberg, A. G. Holder
"Analytic Centers and Repelling Inequalities," CCM No. 142, Center for Computational Mathematics, University of Colorado at Denver, CO 1999.

Robert M. Freund and Jorge R. Vera
"On the complexity of computing estimates of condition measures of a conic linear system," Technical Report 4/99, Dept. of Industrial and System Engineering, Catholic University of Chile, 1999.

Margareta Halicka
"Two simple proofs of analyticity of the central path in linear programming," Mathematics Preprint No. M198, Faculty of Mathematics and Physics, Comenius University, Bratislava, Slovakia

S. Vavasis
"A note on efficient computation of the gradient in semidefinite programming," Department of Computer Science, Cornell University, September 14, 1999

L. Mosheyev and M. Zibulevsky
"Penalty/Barrier Multiplier Algorithm for Semidefinite Programming," Preprint, September, 1999

Sam Burer, Renato Monteiro, Yin Zhang
"Solving Semidefinite Programs via Nonlinear Programming. Part I: Transformations and Derivatives," Technical Report TR99-17 Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, USA

James V. Burke and Michael L. Overton
"Variational Analysis of Non-Lipschitz Spectral Functions," NYU Computer Science Dept Technical Report 790. Submitted to Mathematical Programming.

James V. Burke, Adrian S. Lewis and Michael L. Overton
"Optimizing Matrix Stability," NYU Computer Science Dept Technical Report 791. Submitted to Proceedings of the AMS.

Angel Sanchez-Paulo R. Oliveira-Marcos A. dos Santos
"Recovery of the Analytic Center in Perturbed Quadratic Regions and Applications," Relatorio de Pesquisa/UFRRJ-DEMAT-LESCMA-RP 002-99/09

Changhui Cris Choi and Yinyu Ye
"Application of Semidefinite Programming to Circuit Partitioning," Department of Management Sciences The University of Iowa Iowa City, Iowa 52242, U.S.A.

Xinwei Liu and Gongyun Zhao
"A decomposition method based on SQP for a class of multistage nonlinear stochastic programs," Research report, Department of Mathematics, National University of Singapore, Singapore 119260

Sam Burer, Renato D.C. Monteiro and Yin Zhang
"Solving Semidefinite Programs via Nonlinear Programming Part II: Interior Point Methods for a Subclass of SDPs," Technical Report TR99-23, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005.

P. R. Oliveira and M. A. dos Santos
"Using analytic center and cutting planes methods for nonsmooth convex programming," Submitted to Lecture Notes in Economics and Mathematical Sciences, V. H. Nguyen, J. J. Strodiot and P. Tosssings, ed.

Miguel Anjos and Henry Wolkowicz
"A strengthened SDP relaxation via a second lifting for the MAX-CUT problem," Technical Report CORR-55 October, 1999 University of Waterloo Department of Combinatorics and Optimization Waterloo, Ontario N2L 3G1, Canada

O. P. Ferreira and Oliveira, P. R.
"The Proximal Point Algorithm in Riemannian Manifolds," T. R. ES-453 PESC/COPPE Federal University of Rio de Janeiro 09/97, revised 10/99.

Raphael Hauser
"Self-Scaled Barrier Functions: Decomposition and Classification," DAMTP-Report NA1999/13; Department of Applied Mathematics and Theoretical Physics, Silver Street, University of Cambridge, Cambridge CB3 9EW, England; October 1999.

Raphael Hauser
"Square-root fields and the V-space approach to primal-dual interior-point methods for self-scaled conic programming," Numerical Analysis Report DAMTP 1999/NA14, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW, England, November, 1999.

Yinyu Ye and Jiawei Zhang
".602 Approximation of the Complement of Min-Bisection," Working Paper, Department of Management Sciences, Henry B. Tippie College of Business, The University of Iowa, Iowa City, Iowa 52242.

R.J. Vanderbei and H. Yurttan Benson
"On Formulating Semidefinite Programming Problems as Smooth Convex Nonlinear Optimization Problems ," ORFE 99-01, Dept. of Operations Research and Financial Engineering, Princeton University, Princeton NJ

Yinyu Ye and Jiawei Zhang
".519 Approximation of Dense-n/2-Subgraph," Working Paper, Department of Management Sciences, Henry B. Tippie College of Business, The University of Iowa, Iowa City, Iowa 52242.

Raphael Hauser
"Target Directions for Primal-Dual Interior-Point Methods for Self-Scaled Conic Programming," Numerical Analysis Report DAMTP 1999/NA15, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England CB3 9EW.

Raphael Hauser
"Primal-Dual Symmetric Scale-Invariant Square-Root Fields for Isotropic Self-Scaled Barrier Functionals," Numerical Analysis Report DAMTP 1999/NA16, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England CB3 9EW.

Raphael Hauser
"Nesterov-Todd Directions are Newton Directions," Numerical Analysis Report DAMTP 1999/NA17, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England CB3 9EW.

Samuel Burer, Renato D.C. Monteiro, Yin Zhang
"Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation," Technical Report TR99-27, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005.

E. Alper Yildirim and Michael J. Todd
"Sensitivity analysis in linear programming and semidefinite programming using interior-point methods," Technical Report No. 1253, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801

C. Helmberg and K.C. Kiwiel
"A Spectral Bundle Method with Bounds," Preprint SC 99-37, Konrad-Zuse-Zentrum fuer Informationstechnik Berlin, 14195 Berlin, Germany, December 1999.

Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota and Kazuhide Nakata
"Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework," Research Report B-358, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan. (Also issued as RIMS Preprint No. 1264, Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan.) December 1999.

J. Peng, C. Roos and T. Terlaky
"A new class of polynomial primal-dual methods for linear and semidefinite optimization," Faculty of Information Technology and Systems, Delft University of Technology, P.O.Box 5031, 2600 GA Delft, The Netherlands, December, 1999.

Florian A. Potra
"Q-superlinear convergence of the iterates in primal-dual interior-point methods," Working Paper, University of Maryland Baltimore County, December 1999.

Jie Sun, Kim-Chuan Toh, and Gongyun Zhao
"An Analytic Center Cutting Plane Method For Semidefinite Feasibility Problems," Research Report No 766, Department of Mathematics, National University of Singapore, January 2000.

Han, Ye and Zhang
"Approximation of Dense-k-Subgraph," Working Paper, Department of Management Sciences, Henry B. Tippie College of Business, The University of Iowa, Iowa City, IA 52242, USA. February, 2000.

Han, Ye, Zhang and Zhang
"On Approximation of Max-Vertex-Cover," Working Paper, Department of Management Sciences, Henry B. Tippie College of Business, The University of Iowa, Iowa City, IA 52242, USA. February, 2000.

Andreas Wachter and Lorenz T. Biegler
"Failure of Global Convergence for a Class of Interior Point Methods for Nonlinear Programming," CAPD Technical Report B-99-07, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA (December 1999)

E. Alper Yildirim and Stephen J. Wright
"Warm-start strategies in interior-point methods for linear programming}," Technical Report 1258, School of Operations Research and Industrial Engineering, Cornell University; and Preprint MCS-P799-0300, Mathematics and Computer Science Division, Argonne National Laboratory, March, 2000.

L. Faybusovich and R. Arana
"A long-step primal-dual algorithm for the symmetric programming problem," University of Notre Dame, December 1999.

Miguel F. Anjos and Henry Wolkowicz
"A Tight Semidefinite Relaxation of the Cut Polytope," Research Report CORR 2000-19 (8 March 2000), Department of Combinatorics and Optimization, University of Waterloo.

J. Peng, C. Roos and T. Terlaky
"Self-Regular Proximities and New Search Directions for Linear and Semidefinite Optimization," Preprint, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada, March 2000.

Weichung Wang and Dianne P. O'Leary
"Adaptive Use of Iterative Methods in Predictor-Corrector Interior Point Methods for Linear Programming," Computer Science Department Report CS-TR-4011, Institute for Advanced Computer Studies Report UMIACS-TR-99-21, University of Maryland, April 1999.

Raphael Hauser
"Self-Scaled Barriers for Semidefinite Programming," Numerical Analysis Report DAMTP 2000/NA02, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England CB3 9EW.

C. Choi and Y. Ye
"Solving Sparse Semidefinite Programs Using the Dual Scaling Algorithm with an Iterative Solver," Working Paper, Department of Management Sciences The University of Iowa Iowa City, Iowa 52242, U.S.A., March 2000

N.I.M. Gould, D. Orban, A. Sartenaer, and Ph.L. Toint
"Superlinear convergence of primal-dual interior point algorithms for nonlinear programming," Cerfacs technical report TR/PA/00/20, April 2000. CERFACS - Parallel Algorithms Project 42, Avenue Gaspard Coriolis 31057 Toulouse Cedex 1 - FRANCE.

R.Q. do Nascimento and P. R. Oliveira
"A Globally Convergent Infeasible Interior Point Method for Linear Constrained Convex Programming ," R.T. PESC/COPPE-Federal University of Rio de Janeiro C.P. 68511, 20771-421, Rio de Janeiro, Brazil, 04/2000.

Gabor Pataki
"A Simple Derivation of a Facial Reduction Algorithm, and Extended Dual Systems," Technical Report, Department of IE/OR, Columbia University, April, 2000.

Venansius Baryamureeba
"On Solving Large Sparse Linear Systems arising from Linear Programming and Linear Regression," Ph.D Thesis, March 2000, Department of Informatics, University of Bergen, Post Box 7800, 5020 Bergen, Norway.

Marcelo Marazzi and Jorge Nocedal
"Feasibility Control in Nonlinear Optimization," OTC 2000/4 Optimization Technology Center, March, 2000.

"On the quality of semidefinite approximations of uncertain semidefinite programs affected by box uncertainty," Research report #2/00, April 2000, MINERVA Optimization Center, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel

Faranak Sharifi Mokhtarian and Jean-Louis Goffin
"An Analytic Center Quadratic Cut Method for the Convex Quadratic Feasibility Problem.," GERAD Technical Report G-2000-18, 19 pp, April 2000.

Anders Forsgren and Göran Sporre
"On weighted linear least-squares problems related to interior methods for convex quadratic programming," Report TRITA-MAT-2000-OS11, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden, 2000.

Ernst-Peter Beisel and Manfred Mendel
"Effective Big-M Procedures for Interior Point Methods," Bergische Universitaet GHS Wuppertal, Germany April 2000.

Fernanda M. P. Raupp and Wilfredo Sosa
"An analytic center cutting plane algorithm for finding equilibrium points," Technical Report 07/2000 LNCC - MCT - Brazil.

Jackie C. K. Ho and Levent Tuncel
"Reconciliation of Various Complexity and Condition Measures for Linear Programming Problems and a Generalization of Tardos' Theorem," Research Report CORR2000-33, Department of Combinatorics and Optimization, University of Waterloo, Ontario, Canada, June 12, 2000.

Marina Epelman and Robert M. Freund
"Pre-Conditioners and Relations between Different Measures of Conditioning for Conic Linear Systems," MIT Operations Research Center Working Paper OR344-00.

Masakazu Muramatsu
"On Commutative Class of Search Directions for Linear Programming over Symmetric Cones," Report CS-00-02, Department of Computer Science, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585 Japan.

Stefan H. Schmieta
"Complete Classification of Self-scaled Barrier Functions," TR-2000-01 (July 2000), CORC, Columbia University, New York, NY.

Fernanda M. P. Raupp and Clovis C. Gonzaga
"A Center Cutting Plane Algorithm for a Likelihood Estimate Problem," Technical Report 12/2000 LNCC - MCT - Brazil.

Yang, Ye and Zhang
"Improved Approximation for Max Set Splitting and Max NAE SAT," Working Paper, Department of Management Sciences, The University of Iowa, Iowa City, IA 52242, USA, August, 2000.

Yang, Ye and Zhang
"An Approximation Algorithm for the Two-Parallel Machines Scheduling Problem with Capacity Constraints," Working Paper, Department of Management Sciences, University of Iowa, IA 52242, USA, August, 2000.

Y. Kanno, M. Ohsaki and N. Katoh
"Symmetricity of the Solution of Semidefinite Program ," AIS Reserch Report 00-01, Architectural Information Systems Laboratory, Kyoto University, Sakyo, Kyoto 606-8501, Japan, July, 2000.

Ernst-Peter Beisel, Manfred Mendel
"Controlled Potential Reduction Methods for Linear Programming," Fachbereich 7 Mathematik Bergische Universitaet GHS Gaußstraße 20 D-42097 Wuppertal, April 2000

Kim-Chuan Toh and Masakazu Kojima
"Solving some large scale semidefinite programs via the conjugate residual method," Research Report, Department of Mathematics, National University of Singapore, August 2000

Olivier Epelly, Jacek Gondzio and Jean-Philippe Vial
"An interior point solver for smooth convex optimization with an application to environmental-energy-economic models," Logilab Technical Report 2000.08, Department of Management Studies, University of Geneva, Switzerland

Allen Holder
"Designing Radiotherapy Plans with Elastic Constraints and Interior Point Methods," Trinity University, Mathematics Technical Report #49, August, 2000.

N. I. M. Gould, D. Orban, A. Sartenaer and Ph. L. Toint
"Componentwise fast convergence in the solution of full-rank systems of nonlinear equations," Tech Report TR_PA_00_56 CERFACS - 42, Avenue Gaspard Coriolis 31057 Toulouse Cedex 1. France. September 2000.

Jordi Castro and Antonio Frangioni
" A parallel implementation of an interior-point algorithm for multicommodity network flows," Report DR 2000-06, Statistics and Operations Research Dept, Universitat Politecnica de Catalunya, Barcelona (Spain).

Christoph Helmberg
"Semidefinite Programming for Combinatorial Optimization," Habilitationsschrift, TU Berlin, January 2000. ZIB-Report ZR-00-34, Konrad-Zuse-Zentrum Berlin, Takustrasse 7, D-14195 Berlin, Germany, October 2000.

Ernst-Peter Beisel and Manfred Mendel
"Controlled Potential Reduction Methods for linear Programming," Technical report, Bergische Universitaet GHS Wuppertal, Germany

Samuel Burer, Renato Monteiro, and Yin Zhang
"Rank-Two Relaxation Heuristics for Max-Cut and Other Binary Quadratic Programs," Technical Report TR00-33 Department of Computational and Applied Mathematics Rice University, Houston, Texas 77005

Florian A. Potra
"The Mizuno-Todd-Ye algorithm in a larger neighborhood of the central path," Preprint. Department of Mathematics and Statistics, University of Maryland Baltimore County. November 2000.

Mituhiro Fukuda and Masakazu Kojima
"Interior-Point Methods for Lagrangian Duals of Semidefinite Programs," Research Report B-365, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan, December 2000.

J. Peng, C. Roos, T. Terlaky and A. Yoshise
"Self-regular proximities and new search directions for nonlinear $P_*(\kappa)$ complementarity problems," Preprint, Faculty of Information Technology and Systems, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands.

Jacek Gondzio and Robert Sarkissian
"Parallel Interior Point Solver for Structured Linear Programs ," Technical Report MS-00-025, Department of Mathematics and Statistics, The University of Edinburgh, Scotland. December 4, 2000.

E. D. Andersen, C. Roos, and T. Terlaky
"On implementing a primal-dual interior-point method for conic quadratic optimization," Helsinki School of Economics and Business Administration, Working papers, W-274, December 2000.

Gerald Gruber, Franz Rendl
"Computational experience with stable set relaxations ," Research Report, Department of Mathematics, University of Klagenfurt, Austria, December 2000

Gerald Gruber
"On Semidefinite Programming and Applications in Combinatorial Optimization," PhD thesis, University of Technology, Graz, Austria, 2000. Shaker Verlag, Aachen - Maastricht, ISBN 3-8265-7541-5.

E. Alper Yildirim and Michael J. Todd
"An Interior-Point Approach to Sensitivity Analysis in Degenerate Linear Programs ," Technical Report No. 1268, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801, December 2000.

J. Peng, C. Roos, and T. Terlaky
"New primal-dual algorithms for second-order conic optimization based on self-regular proximities," Technical Report, Faculty of Information Technology and Systems, Delft University of Technology, 2628 CD, Mekelweg, Delft, The Netherlands

R. Byrd, J. Nocedal, and R. Waltz
"Feasible Interior Methods Using Slacks for Nonlinear Optimization," Report OTC 2000/11 Optimization Technology Center, November 2000.

J.L. Morales, J. Nocedal, R. Waltz, G. Liu, J.P. Goux
"Assessing the Potential of Interior Methods for Nonlinear Optimization," Report OTC 2001/4, Optimization Technology Center, Northwestern University, March, 2001.

Samuel Burer, Renato D.C. Monteiro
"A Nonlinear Programming Algorithm for Solving Semidefinite Programs via Low-rank Factorization," School of ISyE Georgia Tech Atlanta, GA 30332 March, 2001.

Florian A. Potra
"A path-following method for linear complementarity problems based on the affine invariant Kantorovich Theorem," ZIB-Report 00-30, August 2000, Konrad-Zuse-Zentrum, Berlin, 2000

Leonid Faybusovich
"Self-concordant barriers for cones generated by Chebyshev systems," Technical Report, January 2001.

Raphael Hauser and Yongdo Lim
"Self-scaled barriers for irreducible symmetric cones," Numerical Analysis Report DAMTP 2001/NA04, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England CB3 9EW. April 2001.

Raphael Hauser and Osman Guler
"Self-scaled barrier functions on symmetric cones and their classification," Numerical Analysis Report DAMTP 2001/NA03, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England CB3 9EW. March 2001.

Mituhiro Fukuda, Masakazu Kojima, and Masayuki Shida
"Lagrangian dual interior-point methods for semidefinite programs," Research Report B-369, Dept. Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro, Tokyo 152-8552 Japan, March 2001.

R. Byrd, M. Marazzi, J. Nocedal
"On the Convergence of Newton Iterations to Non-Stationary Points," Report OTC 2001/7 Optimization Technology Center, April, 2001.

Florian A. Potra
"A superlinearly convergent predictor-corrector method for degenerate LCP in a wide neighborhood of the central path with $O(\sqrt{n}L)$-iteration complexity," Preprint, UMBC, April 2001.

S. Burer, R.D.C. Monteiro, and Y. Zhang
"A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs," Working paper, School of ISyE, Georgia Tech, Atlanta, GA, USA, June 2001.

Kartik Krishnan and John Mitchell
"A linear programming (LP) approach to semidefinite programming (SDP) problems," Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110, 8th Street, Troy, NY, 12180, May 2001.

Miguel F. Anjos and Henry Wolkowicz
"Geometry of Semidefinite Max-Cut Relaxations via Ranks ," Research Report CORR 2001-39, Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

M. Halicka, E. de Klerk, C. Roos
"On the convergence of the central path in semidefinite optimization," Technical report, Faculty ITS, Delft University of Technology, Delft, The Netherlands. June, 2001.

E. Alper Yildirim
"An Interior-Point Perspective on Sensitivity Analysis in Semidefinite Programming," Technical Report No. 1289, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801.

John E. Mitchell
"Polynomial interior point cutting plane methods," Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 USA. July, 2001.

Margareta Halicka
"Analyticity of the central path at the boundary point in semidefinite programming," Technical report, Faculty Matematics, Physics and Informatics, Comenius University, Bratislava.

J. Gondzio and A. Grothey
"Re-optimization with the Primal-Dual Interior Point Method," Technical Report MS-01-004 Department of Mathematics and Statistics, The University of Edinburgh, Scotland. July, 2001.