DUALITY RESULTS FOR CONIC CONVEX PROGRAMMING

Z.-Q. Luo, J.F. Sturm and S. Zhang

This paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone in finite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this paper include Gordon-Stiemke type theorems, Farkas type theorems, perfect duality, Slater condition, regularization, Ramana's duality, and approximate dualities. The dual representations of various convex sets, convex cones and conic convex programs are also discussed.

Keywords: Conic convex programming, duality, semidefinite programming.

AMS subject classification: 90C25, 15A39, 15A45, 90C05.

Report 9719/A, April 1997.
Econometric Institute EUR, P.O. Box 1738, 3000 DR, The Netherlands.

Contact: sturm@few.eur.nl


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