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A Minimax-Program-Based Approach for Robust Fractional Multi-Objective Optimization

Author

Listed:
  • Henan Li

    (Academy for Advanced Interdisciplinary Studies, Northeast Normal University, Changchun 130024, China)

  • Zhe Hong

    (Department of Mathematics, Yanbian University, Yanji 133002, China)

  • Do Sang Kim

    (Department of Applied Mathematics, Pukyong Natinal University, Busan 48513, Republic of Korea)

Abstract

In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of generalized convex functions. Additionally, we formulate a dual problem to the primal one and examine duality relations between them. In our results, by using the obtained results, we obtain necessary and sufficient optimality conditions for a class of robust fractional multi-objective optimization problems.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2475-:d:1453804
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    Full references (including those not matched with items on IDEAS)

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