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Optimality and duality in nonsmooth composite vector optimization and applications

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  • Thai Doan Chuong

    (Ton Duc Thang University
    Ton Duc Thang University)

Abstract

This article is devoted to the study of a nonsmooth composite vector optimization problem (P for brevity). We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of (P). Sufficient conditions for the existence of such solutions to (P) are also provided by means of proposing the use of (strictly) generalized convex composite vector functions with respect to a cone. We also state a dual problem to (P) and explore weak, strong and converse duality relations. In addition, applications to a multiobjective approximation problem and a composite multiobjective problem with linear operators are deployed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:296:y:2021:i:1:d:10.1007_s10479-019-03349-1
    DOI: 10.1007/s10479-019-03349-1
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    References listed on IDEAS

    as
    1. Thai Chuong & Do Kim, 2014. "Optimality conditions and duality in nonsmooth multiobjective optimization problems," Annals of Operations Research, Springer, vol. 217(1), pages 117-136, June.
    2. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    3. 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.
    4. Thai Doan Chuong & Do Sang Kim, 2017. "Nondifferentiable minimax programming problems with applications," Annals of Operations Research, Springer, vol. 251(1), pages 73-87, April.
    5. Jae Hyoung Lee & Gue Myung Lee, 2018. "On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems," Annals of Operations Research, Springer, vol. 269(1), pages 419-438, October.
    6. Thai Doan Chuong & Do Sang Kim, 2016. "A class of nonsmooth fractional multiobjective optimization problems," Annals of Operations Research, Springer, vol. 244(2), pages 367-383, September.
    7. Thai Doan Chuong & Do Sang Kim, 2014. "Nonsmooth Semi-infinite Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 748-762, March.
    8. S. K. Suneja & Sunila Sharma & Priyanka Yadav, 2018. "Generalized higher-order cone-convex functions and higher-order duality in vector optimization," Annals of Operations Research, Springer, vol. 269(1), pages 709-725, October.
    9. Jae Hyoung Lee & Liguo Jiao, 2018. "Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 428-455, February.
    10. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    11. Thai Doan Chuong, 2019. "Optimality and Duality in Nonsmooth Conic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 471-489, November.
    Full references (including those not matched with items on IDEAS)

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