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Optimality and duality in nonsmooth composite vector optimization and applications

  • S.I.: MOPGP 2017
  • Published:
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Abstract

This article is devoted to the study of a nonsmooth composite vector optimization problem (P for brevity). We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of (P). Sufficient conditions for the existence of such solutions to (P) are also provided by means of proposing the use of (strictly) generalized convex composite vector functions with respect to a cone. We also state a dual problem to (P) and explore weak, strong and converse duality relations. In addition, applications to a multiobjective approximation problem and a composite multiobjective problem with linear operators are deployed.

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Acknowledgements

The author is indebted to the three referees for helpful remarks and suggestions, which greatly improved the quality of the paper.

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Authors and Affiliations

  1. Optimization and Applications Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

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  1. Thai Doan Chuong
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Correspondence to Thai Doan Chuong.

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Dedicated to Professor Gue Myung Lee on the occasion of his 65th birthday.

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Chuong, T.D. Optimality and duality in nonsmooth composite vector optimization and applications. Ann Oper Res 296, 755–777 (2021). https://doi.org/10.1007/s10479-019-03349-1

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  • DOI: https://doi.org/10.1007/s10479-019-03349-1

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