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

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  • Phan Khanh
  • Le Tung

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. Copyright Springer Science+Business Media New York 2013

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  • Phan Khanh & Le Tung, 2013. "First and second-order optimality conditions using approximations for vector equilibrium problems with constraints," Journal of Global Optimization, Springer, vol. 55(4), pages 901-920, April.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:4:p:901-920
    DOI: 10.1007/s10898-012-9984-2
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    References listed on IDEAS

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    1. A. Jourani & L. Thibault, 1993. "Approximations and Metric Regularity in Mathematical Programming in Banach Space," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 390-401, May.
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    Cited by:

    1. Nguyen Xuan Duy Bao & Phan Quoc Khanh & Nguyen Minh Tung, 2022. "Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(1), pages 205-228, September.

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