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Optimality conditions for nonsmooth multiobjective bilevel optimization problems

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  • Thai Doan Chuong

    (University of New South Wales)

Abstract

This article is devoted to the study of a nonsmooth multiobjective bilevel optimization problem, which involves the vector-valued objective functions in both levels of the considered program. We first formulate a relaxation multiobjective formulation for the multiobjective bilevel problem and examine the relationships of solutions between them. We then establish Fritz John (FJ) and Karush–Kuhn–Tucker (KKT) necessary conditions for the nonsmooth multiobjective bilevel optimization problem via its relaxation. This is done by studying a related multiobjective optimization problem with operator constraints.

Suggested Citation

  • Thai Doan Chuong, 2020. "Optimality conditions for nonsmooth multiobjective bilevel optimization problems," Annals of Operations Research, Springer, vol. 287(2), pages 617-642, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-017-2734-6
    DOI: 10.1007/s10479-017-2734-6
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    Cited by:

    1. Thai Doan Chuong & Xinghuo Yu & Andrew Eberhard & Chaojie Li & Chen Liu, 2024. "Hierarchy relaxations for robust equilibrium constrained polynomial problems and applications to electric vehicle charging scheduling," Journal of Global Optimization, Springer, vol. 90(3), pages 781-811, November.
    2. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.

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