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Optimality conditions in terms of contingent epiderivatives for strict local Pareto minima in vector optimization problems with constraints

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Abstract

In this paper, primal and dual necessary/sufficient optimality conditions are investigated for vector optimization problem with set, cone and equality constraints. We establish some necessary optimality conditions for strict local Pareto minima in terms of contingent derivatives, contingent epiderivatives and contingent hypoderivatives with steady functions in Banach spaces to such problem. Under suitable assumptions, necessary optimality conditions become sufficient optimality conditions. Examples illustrate the applicability of the obtained results.

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Acknowledgements

The authors would like to express many thanks to two anonymous referees for careful reading of the manuscript, which improved the paper in its present form. Addionally, the authors are grateful to the editors for sending our manuscript to reviewers.

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Authors and Affiliations

  1. Department of Mathematics, Quangnam University, 102 Hung Vuong, 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 conditions in terms of contingent epiderivatives for strict local Pareto minima in vector optimization problems with constraints. Positivity 25, 1737–1760 (2021). https://doi.org/10.1007/s11117-021-00842-5

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  • DOI: https://doi.org/10.1007/s11117-021-00842-5

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