Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Vaithilingam Jeyakumar

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

jeya@maths.unsw.edu.au

Sangho Kum

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

shkum@chungbuk.ac.kr

Gue Myung Lee

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

gmlee@pknu.ac.kr

Keywords

  • Farkas lemma
  • cone-convex systems
  • strong duality
  • closed cone condition
  • second-order cone programming

Suggested citation

V. Jeyakumar, S. Kum, G. M. Lee. “Necessary and Sufficient Conditions for Farkas' Lemma for Cone Systems and Second-Order Cone Programming Duality.” Journal of Convex Analysis 15 (2008), No. 1, 63–71. https://doi.org/10.68381/jca15005

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press.