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Generalized Stampacchia Vector Variational-Like Inequalities and Vector Optimization Problems Involving Set-Valued Maps

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  • Yanfei Chai
  • Sanyang Liu
  • Guotao Wang

Abstract

We first obtain that subdifferentials of set-valued mapping from finite-dimensional spaces to finite-dimensional possess certain relaxed compactness. Then using this weak compactness, we establish gap functions for generalized Stampacchia vector variational-like inequalities which are defined by means of subdifferentials. Finally, an existence result of generalized weakly efficient solutions for vector optimization problem involving a subdifferentiable and preinvex set-valued mapping is established by exploiting the existence of a solution for the weak formulation of the generalized Stampacchia vector variational-like inequality via a Fan-KKM lemma.

Suggested Citation

  • Yanfei Chai & Sanyang Liu & Guotao Wang, 2014. "Generalized Stampacchia Vector Variational-Like Inequalities and Vector Optimization Problems Involving Set-Valued Maps," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, August.
    • Handle: RePEc:hin:jnlaaa:948270
    DOI: 10.1155/2014/948270
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