PROXIMAL POINT ALGORITHMS AND FOUR RESOLVENTS OF NONLINEAR OPERATORS OF MONOTONE TYPE IN BANACH SPACES

作     者：Takahashi, Wataru 

作者机构：Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku Tokyo 1528552 Japan 

出 版 物：《TAIWANESE JOURNAL OF MATHEMATICS》 (Taiwanese J. Math.)

年 卷 期：2008年第12卷第8期

页      面：1883-1910页

核心收录：

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

主　　题：Banach space Proximal point algorithm Resolvent Nonexpansive mapping Maximal monotone operator Retraction Projection Convex optimization 

摘      要：In this article, motivated by Rockafellar s proximal point algorithm in Hilbert spaces, we discuss various weak and strong convergence theorems for resolvents of accretive operators and maximal monotone operators which are connected with the proximal point algorithm. We first deal with proximal point algorithms in Hilbert spaces. Then, we consider weak and strong convergence theorems for resolvents of accretive operators in Banach spaces which generalize the results in Hilbert spaces. Further, we deal with weak and strong convergence theorems for three types of resolvents of maximal monotone operators in Banach spaces which are related to proximal point algorithms. Finally, in Section 7, we apply some results obtained in Banach spaces to the problem of finding minimizers of convex functions in Banach spaces.