Regularized Symmetric Indefinite Systems in Interior Point Methods for Linear and Quadratic Optimization

Anna Altman and Jacek Gondzio

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraints. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and symmetric indefinite systems are described. They transform the latter to quasidefinite systems known to be strongly factorizable to a form of Cholesky-like factorization. Two different regularization techniques {\it primal} and {\it dual} suit very well the (infeasible) primal-dual interior point algorithm. This particular algorithm with an extension of multiple centrality correctors is implemented in our solver HOPDM. Computational results are given to illustrate the potential advantages of the approach applied to the solution of very large linear and convex quadratic programs.

Logilab Technical Report 98.6, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4, Switzerland, March 1998.