Complete characterizations of stable Farkas’ lemma and cone-convex programming duality

Authors:
V. Jeyakumar;G. M. Lee
Affiliations:
University of New South Wales, Department of Applied Mathematics, 2052, Sydney, Australia;Pukyong National University, Department of Applied Mathematics, 608-737, Pusan, South Korea
Venue:
Mathematical Programming: Series A and B
Year:
2008

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Abstract

We establish necessary and sufficient conditions for a stable Farkas’ lemma. We then derive necessary and sufficient conditions for a stable duality of a cone-convex optimization problem, where strong duality holds for each linear perturbation of a given convex objective function. As an application, we obtain stable duality results for convex semi-definite programs and convex second-order cone programs.