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Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints

Author

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  • Tran Su

    (Quang Nam University)

  • Dinh Dieu Hang

    (Thai Nguyen University of Information and Communication Technology)

Abstract

In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aqjoor:v:20:y:2022:i:1:d:10.1007_s10288-020-00470-x
    DOI: 10.1007/s10288-020-00470-x
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    References listed on IDEAS

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    1. P. Khanh & L. Tung, 2015. "Erratum to: 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 618-618, July.
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