Abstract and Applied Analysis

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

Yanfei Chai, Sanyang Liu, and Guotao Wang

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 948270, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278542

Digital Object Identifier
doi:10.1155/2014/948270

Mathematical Reviews number (MathSciNet)
MR3256266

Zentralblatt MATH identifier
07023374

Citation

Chai, Yanfei; Liu, Sanyang; Wang, Guotao. Generalized Stampacchia Vector Variational-Like Inequalities and Vector Optimization Problems Involving Set-Valued Maps. Abstr. Appl. Anal. 2014 (2014), Article ID 948270, 8 pages. doi:10.1155/2014/948270. https://projecteuclid.org/euclid.aaa/1412278542


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