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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia

    V. Jeyakumar

  2. Department of Applied Mathematics, Pukyong National University, Pusan, 608-737, South Korea

    G. M. Lee

Authors
  1. V. Jeyakumar
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  2. G. M. Lee
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Corresponding author

Correspondence to V. Jeyakumar.

Additional information

The authors are grateful to the referees for their valuable suggestions and helpful detailed comments which have contributed to the final preparation of the paper. The first author was supported by the Australian Research Council Linkage Program. The second author was supported by the Basic Research Program of KOSEF (Grant No. R01-2006-000-10211-0).

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Jeyakumar, V., Lee, G.M. Complete characterizations of stable Farkas’ lemma and cone-convex programming duality. Math. Program. 114, 335–347 (2008). https://doi.org/10.1007/s10107-007-0104-x

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  • DOI: https://doi.org/10.1007/s10107-007-0104-x

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