Weak and strong convergence theorems for maximal monotone operators in a Banach space

作     者：Kamimura, S Kohsaka, F Takahashi, W 

作者机构：Hitotsubashi Univ Grad Sch Int Corp Strategy Chiyoda Ku Tokyo 1018439 Japan Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku Tokyo 1528552 Japan 

出 版 物：《SET-VALUED ANALYSIS》 (集值分析)

年 卷 期：2004年第12卷第4期

页      面：417-429页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：convex minimization problem maximal monotone operator proximal point algorithm resolvent uniformly convex Banach space 

摘      要：In this paper, we introduce an iterative sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim. 14 (1976), 877-898] and Kamimura and Takahashi [J. Approx. Theory 106 (2000), 226-2401. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem.