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Nondifferentiable minimax programming problems with applications

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  • Thai Doan Chuong

    (Saigon University)

  • Do Sang Kim

    (Pukyong National University)

Abstract

This paper is devoted to the study of optimality conditions and duality in nondifferentiable minimax programming problems and applications. Employing some advanced tools of variational analysis and generalized differentiation, we establish new necessary conditions for optimal solutions of a minimax programming problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions to the considered problem are also obtained by way of $$L$$ L -invex-infine functions. We state a dual problem to the primal one and explore weak, strong and converse duality relations between them. In addition, some of these results are applied to a nondifferentiable multiobjective optimization problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:251:y:2017:i:1:d:10.1007_s10479-015-1843-3
    DOI: 10.1007/s10479-015-1843-3
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    References listed on IDEAS

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    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 & 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.
    3. Hang-Chin Lai & Tone-Yau Huang, 2012. "Nondifferentiable minimax fractional programming in complex spaces with parametric duality," Journal of Global Optimization, Springer, vol. 53(2), pages 243-254, June.
    4. S. K. Mishra & N. G. Rueda, 2006. "Second-Order Duality for Nondifferentiable Minimax Programming Involving Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 479-488, September.
    5. 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.
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    Cited by:

    1. D. T. V. An & N. H. Hung & D. T. Ngoan & N. V. Tuyen, 2024. "Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming," Journal of Global Optimization, Springer, vol. 90(1), pages 53-72, September.
    2. 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.
    3. 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.
    4. Henan Li & Zhe Hong & Do Sang Kim, 2024. "A Minimax-Program-Based Approach for Robust Fractional Multi-Objective Optimization," Mathematics, MDPI, vol. 12(16), pages 1-14, August.

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