An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems

Authors:
Jun Li;Nan-Jing Huang
Affiliations:
School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, P.R. China 637002;Department of Mathematics, Sichuan University, Chengdu, Sichuan, P.R. China 610064
Venue:
Journal of Global Optimization
Year:
2007

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Abstract

In this paper, the notion of gap functions is extended from scalar case to vector one. Then, gap functions and generalized functions for several kinds of vector equilibrium problems are shown. As an application, the dual problem of a class of optimization problems with a system of vector equilibrium constraints (in short, OP) is established, the concavity of the dual function, the weak duality of (OP) and the saddle point sufficient condition are derived by using generalized gap functions.