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A class of nonsmooth fractional multiobjective optimization problems

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  • Thai Doan Chuong

    (Saigon University)

  • Do Sang Kim

    (Pukyong National University)

Abstract

This paper focuses on the study of optimality conditions and duality in nonsmooth fractional multiobjective optimization problems. Applying some advanced tools of variational analysis and generalized differentiation, we establish necessary optimality conditions for (weakly) efficient solutions of a fractional multiobjective optimization problem involving inequality and equality constraints. Sufficient optimality conditions for such solutions to the considered problem are also obtained by means of (strictly) generalized convex-affine functions. In addition, we address a dual problem to the primal one and examine duality relations between them.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-016-2130-7
    DOI: 10.1007/s10479-016-2130-7
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    References listed on IDEAS

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    1. D. S. Kim & S. J. Kim & M. H. Kim, 2006. "Optimality and Duality for a Class of Nondifferentiable Multiobjective Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 131-146, April.
    2. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    3. T. Q. Bao & P. Gupta & B. S. Mordukhovich, 2007. "Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 179-203, November.
    4. 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.
    5. 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.
    6. X. J. Long, 2011. "Optimality Conditions and Duality for Nondifferentiable Multiobjective Fractional Programming Problems with (C,α,ρ,d)-convexity," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 197-208, January.
    7. 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. Amal Mekhilef & Mustapha Moulaï & Wassila Drici, 2021. "Solving multi-objective integer indefinite quadratic fractional programs," Annals of Operations Research, Springer, vol. 296(1), pages 821-840, January.
    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. Vo Duc Thinh & Thai Doan Chuong, 2018. "Directionally generalized differentiation for multifunctions and applications to set-valued programming problems," Annals of Operations Research, Springer, vol. 269(1), pages 727-751, October.
    4. 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.
    5. 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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