Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

Authors:
S. J. Li;K. L. Teo;X. Q. Yang;S. Y. Wu
Affiliations:
Department of Information and Computer Sciences, College of Mathematics and Science, Chongqing University, Chongqing, China 400044;Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia 6845;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;Aff4 Aff5
Venue:
Journal of Global Optimization
Year:
2006

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Abstract

This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.