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Optimality conditions for a class of composite multiobjective nonsmooth optimization problems

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  • Li Tang
  • Ke Zhao

Abstract

In this paper, a class of composite multiobjective nonsmooth optimization problems with cone constraints is considered. Necessary optimality conditions for weak minimum are established in terms of Semi-infinite Gordan type theorem. η-generalized null space condition, which is a proper generalization of generalized null space condition, is proposed. Sufficient optimality conditions are obtained for weak minimum, Pareto minimum, Benson’s proper minimum under K-generalized invexity and η-generalized null space condition. Some examples are given to illustrate our main results. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Li Tang & Ke Zhao, 2013. "Optimality conditions for a class of composite multiobjective nonsmooth optimization problems," Journal of Global Optimization, Springer, vol. 57(2), pages 399-414, October.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:2:p:399-414
    DOI: 10.1007/s10898-012-9957-5
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    References listed on IDEAS

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    1. Suneja, S.K. & Khurana, Seema & Vani, 2008. "Generalized nonsmooth invexity over cones in vector optimization," European Journal of Operational Research, Elsevier, vol. 186(1), pages 28-40, April.
    2. Khurana, Seema, 2005. "Symmetric duality in multiobjective programming involving generalized cone-invex functions," European Journal of Operational Research, Elsevier, vol. 165(3), pages 592-597, September.
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    Cited by:

    1. M. Ruiz Galán, 2017. "A theorem of the alternative with an arbitrary number of inequalities and quadratic programming," Journal of Global Optimization, Springer, vol. 69(2), pages 427-442, October.
    2. Thai Doan Chuong, 2021. "Optimality and duality in nonsmooth composite vector optimization and applications," Annals of Operations Research, Springer, vol. 296(1), pages 755-777, January.

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