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Journal of Convex Analysis 15 (2008), No. 1, 063--071
Copyright Heldermann Verlag 2008

Necessary and Sufficient Conditions for Farkas' Lemma for Cone Systems and Second-Order Cone Programming Duality

Vaithilingam Jeyakumar
School of Mathematics, University of New South Wales, Sydney 2052, Australia

Sangho Kum
Dept. of Mathematics Education, Chungbuk National University, Cheongju 361-763, Korea

Gue Myung Lee
Dept. of Applied Mathematics, Pukyong National University, Pusan 608-737, Korea

We present conditions, which completely characterize Farkas' lemma for cone-convex systems, and obtain strong duality characterizations for convex optimization problems. In particular, we establish a necessary and sufficient closed cone condition for the Farkas lemma. As an application, we obtain necessary and sufficient conditions for the strong duality of convex second-order cone programming problems.

Keywords: Farkas lemma, cone-convex systems, strong duality, closed cone condition, second-order cone programming.

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