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Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints

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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.

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Acknowledgements

The authors would like to thank the two anonymous referees and Professor Yves Crama for their valuable comments and suggestions which have improved the final preparation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Quang Nam University, Tamky, Vietnam

    Tran Van Su

  2. Department of Basic Sciences, Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam

    Dinh Dieu Hang

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  1. Tran Van Su
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  2. Dinh Dieu Hang
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Correspondence to Tran Van Su.

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Van Su, T., Hang, D.D. Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints. 4OR-Q J Oper Res 20, 105–137 (2022). https://doi.org/10.1007/s10288-020-00470-x

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  • DOI: https://doi.org/10.1007/s10288-020-00470-x

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