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

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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Correspondence to Nguyen Van Tuyen.

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Son, T.Q., Van Tuyen, N. & Wen, C. 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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Keywords

  • Approximate Pareto solutions
  • Optimality conditions
  • Clarke subdifferential
  • Semi-infinite vector optimization
  • Infinite vector optimization

Mathematics Subject Classification (2010)

  • 41A65
  • 65K10
  • 90C34
  • 90C29
  • 90C46