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Efficient solutions and optimality conditions for vector equilibrium problems

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  • Do Luu
  • Dinh Hang

Abstract

Necessary optimality conditions for efficient solutions of unconstrained and vector equilibrium problems with equality and inequality constraints are derived. Under assumptions on generalized convexity, necessary optimality conditions for efficient solutions become sufficient optimality conditions. Note that it is not required here that the ordering cone in the objective space has a nonempty interior. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Do Luu & Dinh Hang, 2014. "Efficient solutions and optimality conditions for vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 163-177, April.
    • Handle: RePEc:spr:mathme:v:79:y:2014:i:2:p:163-177
    DOI: 10.1007/s00186-013-0457-2
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    References listed on IDEAS

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    1. F. Cammaroto & B. Di Bella, 2005. "Separation Theorem Based on the Quasirelative Interior and Application to Duality Theory," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 223-229, April.
    2. D.E. Ward & G.M. Lee, 2002. "On Relations Between Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 583-596, June.
    3. J. Morgan & M. Romaniello, 2006. "Scalarization and Kuhn-Tucker-Like Conditions for Weak Vector Generalized Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 309-316, August.
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    Citations

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    Cited by:

    1. Tran Van Su, 2018. "New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces," 4OR, Springer, vol. 16(2), pages 173-198, June.
    2. Do Luu, 2016. "Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 643-665, November.
    3. Do Van Luu, 2018. "Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems," Journal of Global Optimization, Springer, vol. 70(2), pages 437-453, February.

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