On the characterization of the solution set for vector equilibrium problem

Volume 10, Issue 11, pp 5881--5895 http://dx.doi.org/10.22436/jnsa.010.11.25

Publication Date: November 24, 2017 Submission Date: July 02, 2017

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Authors

Gang Wang - School of Management Science, Qufu Normal University, Shandong, Rizhao, 276826, China. Lijun Gao - School of Engineering, Qufu Normal University, Shandong, Rizhao, 276826, China.

Abstract

In this article, we investigate the nonemptiness and compactness of the solution set for vector equilibrium problem defined in finite-dimensional spaces. We show that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set provided that \(R_1=\{0\}\) holds. Furthermore, we obtain that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set when coercivity condition holds. As applications, we employ the obtained results to derive Levitin-Polyak well-posedness, stability analysis and connectedness of the solution set of the vector equilibrium problem.

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Keywords

• Vector equilibrium problem
• nonemptiness and compactness
• asymptotic cone
• coercivity condition

MSC

•  90C29
•  90C33

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