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Optimality conditions and duality in nonsmooth multiobjective optimization problems

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  • Thai Chuong
  • Do Kim

Abstract

Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Fréchet subdifferential, the sum rule for the limiting subdifferential and the scalarization formulae of the coderivatives, we establish necessary conditions for (weakly) efficient solutions of a multiobjective optimization problem with inequality and equality constraints. Sufficient conditions for (weakly) efficient solutions of an aforesaid problem are also provided by means of employing L-(strictly) invex-infine functions defined in terms of the limiting subdifferential. In addition, we introduce types of Wolfe and Mond–Weir dual problems and investigate weak/strong duality relations. Copyright Springer Science+Business Media New York 2014

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  • 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.
    • Handle: RePEc:spr:annopr:v:217:y:2014:i:1:p:117-136:10.1007/s10479-014-1552-3
    DOI: 10.1007/s10479-014-1552-3
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    References listed on IDEAS

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    1. S. Askar & A. Tiwari, 2009. "First-order optimality conditions and duality results for multi-objective optimisation problems," Annals of Operations Research, Springer, vol. 172(1), pages 277-289, November.
    2. S. Nobakhtian, 2008. "Generalized (F,ρ)-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 61-68, January.
    3. Altannar Chinchuluun & Dehui Yuan & Panos Pardalos, 2007. "Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity," Annals of Operations Research, Springer, vol. 154(1), pages 133-147, October.
    4. Jin-Chirng Lee & Hang-Chin Lai, 2005. "Parameter-Free Dual Models for Fractional Programming with Generalized Invexity," Annals of Operations Research, Springer, vol. 133(1), pages 47-61, January.
    5. Tadeusz Antczak, 2006. "An Η-Approximation Approach In Nonlinear Vector Optimization With Univex Functions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 525-542.
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    Cited by:

    1. Thai Doan Chuong, 2022. "Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization," Annals of Operations Research, Springer, vol. 311(2), pages 997-1015, April.
    2. 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.
    3. Zhe Hong & Kwan Deok Bae & Do Sang Kim, 2022. "Minimax programming as a tool for studying robust multi-objective optimization problems," Annals of Operations Research, Springer, vol. 319(2), pages 1589-1606, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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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