A PROXIMAL POINT ALGORITHM FOR A SYSTEM OF GENERALIZED MIXED VARIATIONAL INEQUALITIES

作     者：Bo WAN Xuegang ZHAN Bo WAN;Xuegang ZHAN

作者机构：Department of Mathematics and StatisticsChongqing Technology and Business University School of AccountancyChongqing Technology and Business University 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2012年第25卷第5期

页      面：964-972页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the Natural Science Foundation of China under Grant No.11001287 the Natural Science Foundation Project of CSTC under Grant No.2010BB9254 

主　　题：Lipschitz continuity proximal point algorithms relaxed (γ τ)-cocoercivity system ofgeneralized mixed variational inequalities. 

摘      要：This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.