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On optimality conditions and duality for multiobjective optimization with equilibrium constraints

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Abstract

In this paper, we consider nonsmooth multiobjective optimization problems with equilibrium constraints. Necessary/sufficient conditions for optimality in terms of the Michel-Penot subdifferential are established. Then, we propose Wolfe- and Mond–Weir-types of dual problems and investigate duality relations under generalized convexity assumptions. Some examples are provided to illustrate our results.

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Acknowledgements

The first author was supported by Vietnam University - Ho Chi Minh City (VNU-HCM) under Grant no. T2023-20-01. A part of this work was completed during a stay of the authors at the Vietnam Institute for Advanced Study in Mathematics (VIASM). The authors would like to thank VIASM for its hospitality and support. The authors are very much grateful to the editors and the anonymous referees for allowing them to improve the first submission according to their critical and helpful remarks and valuable suggestions.

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Authors and Affiliations

  1. Optimization Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    P. Q. Khanh

  2. Department of Mathematics, College of Natural Sciences, Can Tho University, Can Tho, Vietnam

    L. T. Tung

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  1. P. Q. Khanh
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Correspondence to L. T. Tung.

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Khanh, P.Q., Tung, L.T. On optimality conditions and duality for multiobjective optimization with equilibrium constraints. Positivity 27, 49 (2023). https://doi.org/10.1007/s11117-023-01001-8

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