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First and second-order optimality conditions using approximations for vector equilibrium problems with constraints

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Abstract

We consider various kinds of solutions to nonsmooth vector equilibrium problems with functional constraints. By using first and second-order approximations as generalized derivatives, we establish both necessary and sufficient optimality conditions. Our first-order conditions are shown to be applicable in many cases, where existing ones cannot be used. The second-order conditions are new.

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Authors and Affiliations

  1. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    Phan Quoc Khanh

  2. Department of Mathematics, College of Sciences, Cantho University, Cantho, Vietnam

    Le Thanh Tung

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  1. Phan Quoc Khanh
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  2. Le Thanh Tung
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Correspondence to Phan Quoc Khanh.

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Khanh, P.Q., Tung, L.T. First and second-order optimality conditions using approximations for vector equilibrium problems with constraints. J Glob Optim 55, 901–920 (2013). https://doi.org/10.1007/s10898-012-9984-2

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  • DOI: https://doi.org/10.1007/s10898-012-9984-2

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