A GENERALIZATION OF THE PROXIMAL POINT ALGORITHM

作     者：HA, CD 

作者机构：VIRGINIA COMMONWEALTH UNIVDEPT MATH SCIRICHMONDVA 23284 

出 版 物：《SIAM JOURNAL ON CONTROL AND OPTIMIZATION》 (工业与应用数学会控制与最佳化杂志)

年 卷 期：1990年第28卷第3期

页      面：503-512页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：47H05 49D45 90C25 monotone operator convex programming proximal point algorithm generalized equation 

摘      要：The problem considered in this paper is to find a solution to the generalized equation $0 \in T(x,y)$, where T is a maximal monotone operator on the product $H_1 \times H_2 $ of two Hilbert spaces $H_1 $ and $H_2 $. We give a generalization of the proximal map and the proximal point algorithm in which the proposed iterative procedure is based on just one variable. Applying to convex programming problems, instead of adding a quadratic term for all variables as in the proximal point algorithm, a quadratic term for a subset of variables is added. This paper proves that under a mild assumption our algorithm has the same convergence properties as the regular proximal point algorithm.