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Optimality Conditions for Approximate Pareto Solutions of a Nonsmooth Vector Optimization Problem with an Infinite Number of Constraints

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Abstract

In this paper, we present some new necessary and sufficient optimality conditions in terms of Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of constraints. As a consequence, we obtain optimality conditions for the particular cases of cone-constrained convex vector optimization problems and semidefinite vector optimization problems. Examples are given to illustrate the obtained results.

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Acknowledgments

The authors would like to thank the anonymous referee and the handling Associate Editor for their valuable remarks and detailed suggestions that allowed us to improve the original version.

Funding

The research of Ta Quang Son was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2017.08. The research of Nguyen Van Tuyen was supported by the Ministry of Education and Training of Vietnam (grant number B2018-SP2-14). The research of Ching-Feng Wen was supported by the Taiwan MOST (grant number 107-2115-M-037-001) as well as the grant from Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Taiwan.

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Authors and Affiliations

  1. Faculty of Mathematics and Applications, Saigon University, Ho Chi Minh City, Vietnam

    Ta Quang Son

  2. Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam

    Nguyen Van Tuyen

  3. Center for Fundamental Science, Kaohsiung, Taiwan

    Ching-Feng Wen

  4. Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, Taiwan

    Ching-Feng Wen

  5. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan

    Ching-Feng Wen

Authors
  1. Ta Quang Son
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  2. Nguyen Van Tuyen
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  3. Ching-Feng Wen
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Correspondence to Nguyen Van Tuyen.

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Son, T.Q., Van Tuyen, N. & Wen, CF. Optimality Conditions for Approximate Pareto Solutions of a Nonsmooth Vector Optimization Problem with an Infinite Number of Constraints. Acta Math Vietnam 45, 435–448 (2020). https://doi.org/10.1007/s40306-019-00358-x

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  • DOI: https://doi.org/10.1007/s40306-019-00358-x

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