Hilbert空间中变分不等式组的两步投影算法  

Two-step Projection Methods for Solving a System of General Variational Inequalities in Hilbert Space

作　　者：吴艳秋[1] 夏福全[2] 

机构地区：[1]重庆三峡学院数学与计算机科学学院,重庆万州404000 [2]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2011年第5期615-620,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省教育厅自然科学青年基金(09ZA091)资助项目

摘　　要：变分不等式解的迭代算法是变分不等式理论的重要内容之一,而投影方法是研究变分不等式解的迭代算法的重要方法,已经有着广泛的研究和应用.主要研究Hilbert空间中变分不等式组的近似解问题,给出了变分不等式组解的两步投影算法,在映象T松弛-(γ,r)-余强制的假设条件下,证明了两步投影算法所产生的迭代序列收敛于变分不等式组的解.所获得的结果推广和改进了文献中的一些主要结果.Variational inequalities and variational inclusions are among the most interesting and important mathematical problems and have been studied intensively in the past years since they have wide applications in the optimization and control,economics and transportation equilibrium,engineering science.For these reasons,many existence result and iterative algorithms for various variational inclusion have been studied.The projection methods for variational inequalities,being one of the most important iterative algorithms,has been widely studied.The purpose of this paper is to discuss the approximation solvability of a system of general variational inequalities in Hilbert space.We first introduce the two-step projection methods,and then prove that the convergence of the algorithm for the case that the mapping T satisfies relaxed-（γ,r）-cocoercity.These convergence results generalize and improve the theorem 3.1 in R.V.Verma＇s paper（Comput Math Appl,2009,58：1631-1635.）.

关 键 词：变分不等式组 r-强单调映射 松弛-(γ r)-余强制 

分 类 号：O175.26[理学—数学]