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Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems

Abstract

We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variational-like inequality involving set-valued mappings. We prove some existence results concerned with the weakly efficient solution for the nonconvex and nonsmooth vector optimization problems by using the equivalence and Fan-KKM theorem under some suitable conditions.

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Correspondence to Jong Kyu Kim.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Liu, ZB., Kim, J.K. & Huang, NJ. Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems. J Inequal Appl 2008, 678014 (2008). https://doi.org/10.1155/2008/678014

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  • DOI: https://doi.org/10.1155/2008/678014

Keywords

  • Banach Space
  • Existence Result
  • Suitable Condition
  • Efficient Solution
  • Vector Optimization