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First- and second-order optimality conditions for multiobjective fractional programming

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  • P. Khanh
  • L. Tung

Abstract

We consider nonsmooth multiobjective fractional programming on normed spaces. Using first- and second-order approximations as generalized derivatives, first- and second-order optimality conditions are established. Unlike the existing results, we avoid completely convexity assumptions. Our results can be applied even in infinite-dimensional cases, involving non-Lipschitz maps. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • P. Khanh & L. Tung, 2015. "First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 419-440, July.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:2:p:419-440
    DOI: 10.1007/s11750-014-0347-7
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    References listed on IDEAS

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    1. P. Q. Khanh & N. D. Tuan, 2006. "First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 289-308, August.
    2. Z. A. Liang & H. X. Huang & P. M. Pardalos, 2001. "Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 611-619, September.
    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. A. Jourani & L. Thibault, 1993. "Approximations and Metric Regularity in Mathematical Programming in Banach Space," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 390-401, May.
    5. 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.
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    Cited by:

    1. Tran Su & Dinh Dieu Hang, 2022. "Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints," 4OR, Springer, vol. 20(1), pages 105-137, March.
    2. Soghra Nobakhtian & Narjes Shafiei, 2017. "A Benson type algorithm for nonconvex multiobjective programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 271-287, July.

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