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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:948270
    DOI: 10.1155/2014/948270
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    References listed on IDEAS

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    1. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, June.
    2. J. Baier & J. Jahn, 1999. "On Subdifferentials of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 233-240, January.
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