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Optimality Conditions for Extended Ky Fan Inequality with Cone and Affine Constraints and Their Applications

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Abstract

The purpose of this paper is to establish necessary and sufficient conditions for a point to be solution of an extended Ky Fan inequality. Using a separation theorem for convex sets, involving the quasi-interior of a convex set, we obtain optimality conditions for solutions of the generalized problem with cone and affine constraints. Then the main result is applied to vector optimization problems with cone and affine constraints and to duality theory.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Cluj-Napoca, Str. Constantin Daicoviciu 15, 400020, Cluj-Napoca, Romania

    Adela Capătă

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  1. Adela Capătă
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Correspondence to Adela Capătă.

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Communicated by Igor Konnov.

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Capătă, A. Optimality Conditions for Extended Ky Fan Inequality with Cone and Affine Constraints and Their Applications. J Optim Theory Appl 152, 661–674 (2012). https://doi.org/10.1007/s10957-011-9916-1

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  • DOI: https://doi.org/10.1007/s10957-011-9916-1

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