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Derivatives of the Efficient Point Multifunction in Parametric Vector Optimization Problems

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  • Thai Doan Chuong

    (Saigon University)

Abstract

In this paper, we deal with the sensitivity analysis in vector optimization. More specifically, formulae for inner and outer evaluating the S-derivative of the efficient point multifunction in parametric vector optimization problems are established. These estimating formulae are presented via the set of efficient/weakly efficient points of the S-derivative of the original multifunction, a composite multifunction of the objective function and the constraint mapping. The elaboration of the formulae in vector optimization problems, having multifunction constraints and semiinfinite constraints, is also undertaken. Furthermore, examples are provided for analyzing and illustrating the obtained results.

Suggested Citation

  • Thai Doan Chuong, 2013. "Derivatives of the Efficient Point Multifunction in Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 247-265, February.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:2:d:10.1007_s10957-012-0099-1
    DOI: 10.1007/s10957-012-0099-1
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    References listed on IDEAS

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    1. T. D. Chuong & J. C. Yao, 2010. "Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 77-94, July.
    2. T. Chuong & N. Huy & J. Yao, 2009. "Stability of semi-infinite vector optimization problems under functional perturbations," Computational Optimization and Applications, Springer, vol. 45(4), pages 583-595, December.
    3. Chuong, T.D. & Huy, N.Q. & Yao, J.C., 2010. "Pseudo-Lipschitz property of linear semi-infinite vector optimization problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 639-644, February.
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    Cited by:

    1. Nguyen Thi Toan & Le Quang Thuy, 2023. "S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 240-265, January.
    2. Nguyen Minh Tung & Nguyen Xuan Duy Bao, 2022. "Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations," Journal of Global Optimization, Springer, vol. 83(2), pages 377-402, June.
    3. Thai Doan Chuong & Do Sang Kim, 2018. "Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications," Annals of Operations Research, Springer, vol. 267(1), pages 81-99, August.

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