Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings

Authors:
Nan-Jing Huang;Jun Li;Soon-Yi Wu
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, P.R. China 610064;School of Mathematics and Information, China West Normal University, Nanchong, P.R. China 637002;Institute of Applied Mathematics, National Cheng-Kung University, Tainan, Taiwan 700 and National Center for Theoretical Sciences, Tainan, Taiwan
Venue:
Journal of Global Optimization
Year:
2008

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Abstract

In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore, a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions.