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

Yanfei Chai, Sanyang Liu and Guotao Wang

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/948270

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:948270

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