PROXIMAL DECOMPOSITION ON THE GRAPH OF A MAXIMAL MONOTONE OPERATOR

作     者：MAHEY, P OUALIBOUCH, S TAO, PD 

作者机构：INST INFORMAT & INTELLIGENCE ARTIFICIELLECH-2000 NEUCHATELSWITZERLAND INSALMAIF-76131 MONT ST AIGNANFRANCE 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：1995年第5卷第2期

页      面：454-466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：PROXIMAL POINT ALGORITHM PARTIAL INVERSE CONVEX PROGRAMMING 

摘      要：We present an algorithm to solve: Find (x, y) epsilon A x A perpendicular to such that y epsilon Tx, where A is a subspace and T is a maximal monotone operator. The algorithm is based on the proximal decomposition on the graph of a monotone operator and we show how to recover Spingarn s decomposition method. We give a proof of convergence that does not use the concept of partial inverse and show how to choose a scaling factor to accelerate the convergence in the strongly monotone case. Numerical results performed on quadratic problems confirm the robust behaviour of the algorithm.