Scalarization of approximate solution for vector equilibrium problems

Qiusheng Qiu; Xinmin Yang

doi:10.3934/jimo.2013.9.143

Article Contents

2013, Volume 9, Issue 1: 143-151. Doi: 10.3934/jimo.2013.9.143

This issue Previous Article Optimality conditions and duality in nondifferentiable interval-valued programming Next Article Proximal point algorithm for nonlinear complementarity problem based on the generalized Fischer-Burmeister merit function

Scalarization of approximate solution for vector equilibrium problems

Qiusheng Qiu^1, and
Xinmin Yang^2,

1.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004
2.
Department of Mathematics, Chongqing Normal University, Chongqing, 400047

Received: October 31, 2011

Revised: May 31, 2012

Published: December 2012

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Abstract

In this paper, some scalar characterizations of approximate weakly efficient solutions and approximate Henig efficient solutions for vector equilibrium problems are derived without imposing any convexity assumption on objective functions and feasible set. Meanwhile, the linear scalar characterization of approximate weakly efficient solutions is also established under the conditions of generalized convexity. As an application of the results in this paper, scalar characterizations of weakly efficient solution, Henig efficient solution and super efficient solution for vector equilibrium problems are obtained.

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Mathematics Subject Classification: 90C26, 91B50.

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