Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints

Authors:
Ya-Ping Fang;Rong Hu;Nan-Jing Huang
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;Department of Computational Science, Chengdu University of Information Technology, Chengdu Sichuan, PR China;Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper we generalize the concepts of well-posedness to equilibrium problems and to optimization problems with equilibrium constraints. We establish some metric characterizations of well-posedness for equilibrium problems and for optimization problems with equilibrium constraints. We prove that under suitable conditions, the well-posedness is equivalent to the existence and uniqueness of solutions. The corresponding concepts of well-posedness in the generalized sense are also introduced and investigated for equilibrium problems and for optimization problems with equilibrium constraints.