The Proximal Point Algorithm Revisited

作     者：Dong, Yunda 

作者机构：Zhengzhou Univ Sch Math & Stat Zhengzhou 450001 Peoples R China 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：2014年第161卷第2期

页      面：478-489页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Monotone operator Convex minimization Proximal point algorithm Rate of convergence 

摘      要：In this paper, we consider the proximal point algorithm for the problem of finding zeros of any given maximal monotone operator in an infinite-dimensional Hilbert space. For the usual distance between the origin and the operator s value at each iterate, we put forth a new idea to achieve a new result on the speed at which the distance sequence tends to zero globally, provided that the problem s solution set is nonempty and the sequence of squares of the regularization parameters is nonsummable. We show that it is comparable to a classical result of Br,zis and Lions in general and becomes better whenever the proximal point algorithm does converge strongly. Furthermore, we also reveal its similarity to Guler s classical results in the context of convex minimization in the sense of strictly convex quadratic functions, and we discuss an application to an I mu-approximation solution of the problem above.