Open Access Research

Convergence analysis of projection methods for a new system of general nonconvex variational inequalities

Dao-Jun Wen1*, Xian-Jun Long1 and Qian-Fen Gong2

Author Affiliations

1 College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

2 College of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing 400067, China

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Fixed Point Theory and Applications 2012, 2012:59 doi:10.1186/1687-1812-2012-59

Published: 13 April 2012

Abstract

In this article, we introduce and consider a new system of general nonconvex variational inequalities defined on uniformly prox-regular sets. We establish the equivalence between the new system of general nonconvex variational inequalities and the fixed point problems to analyze an explicit projection method for solving this system. We also consider the convergence of the projection method under some suitable conditions. Results presented in this article improve and extend the previously known results for the variational inequalities and related optimization problems.

MSC (2000): 47J20; 47N10; 49J30.

Keywords:
system of general nonconvex variational inequalities; explicit projection methods; uniform prox-regular set; r-strongly monotone mappings; μ-Lipschitz continuous.