Banach空间中解变分包含问题的超松弛临界点算法  

The Over-relaxed Proximal Point Algorithm for Solving Variational Inclusions in Banach Spaces

作　　者：关金玉[1] 徐永春[1] 何震[2] 

机构地区：[1]河北北方学院数学系,河北张家口075000 [2]河北大学数学与计算机学院,河北保定071002

出　　处：《数学的实践与认识》2010年第13期170-176,共7页Mathematics in Practice and Theory

基　　金：河北省教育厅自然科学项目(2009103);张家口市科学技术研究与发展计划项目(0811024B-5);教育部重点课题(207104)

摘　　要：把Verma关于解变分包含问题的超松弛临界点算法(over-relaxed proximalpoint algorithm)从Hilbert空间扩展为q一致光滑Banach空间.并且导出了更为广义的超松弛临界点算法,在较弱的条件下证明了它的收敛性质.因此,研究结果可以应用于L^p,W^(m,p)(Ω)(p>1)等空间.In this paper we will Verma＇s results on the over-relaxed proximal point algorithm of variational inclusions extent to Banach spaces. It is differ with Verma＇s paper on excepting the restriction that the space X is Hilbert space and other the conditions. We also introduced the generalized over-relaxed proximal point algorithm and showed its the convergence. Thus our research for the variational inclusions can be applied to spaces L^p, W^m,p（Ω）（p 〉 1）.

关 键 词：q-致光滑Banach空间 H—η-增生算子 广义预解算子 变分包含 广义超松弛临界点算法 

分 类 号：O177.2[理学—数学]