Geodesic
Necessary and Sufficient Conditions for Farkas' Lemma for Cone Systems and Second-Order Cone Programming Duality
Journal of convex analysis, Tome 15 (2008) no. 1, pp. 63-71.

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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.
Mots-clés : Farkas lemma, cone-convex systems, strong duality, closed cone condition, second-order cone programming 
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     author = {V. Jeyakumar and S. Kum and G. M. Lee},
     title = {Necessary and {Sufficient} {Conditions} for {Farkas'} {Lemma} for {Cone} {Systems} and {Second-Order} {Cone} {Programming} {Duality}},
     journal = {Journal of convex analysis},
     pages = {63--71},
     publisher = {mathdoc},
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     number = {1},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_1_JCA_2008_15_1_a4/}
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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, Tome 15 (2008) no. 1, pp. 63-71. http://geodesic.mathdoc.fr/item/JCA_2008_15_1_JCA_2008_15_1_a4/