BEST APPROXIMATION FROM THE KUHN-TUCKER SET OF COMPOSITE MONOTONE INCLUSIONS

作     者：Alotaibi, Abdullah Combettes, Patrick L. Shahzad, Naseer 

作者机构：King Abdulaziz Univ Dept Math Jeddah 21413 Saudi Arabia Univ Paris 06 Sorbonne Univ Lab Jacques Louis Lions UMR 7598 F-75005 Paris France 

出 版 物：《NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION》 (数值函数分析与最佳化)

年 卷 期：2015年第36卷第12期

页      面：1513-1532页

核心收录：

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

基　　金：Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah [12-130-1433-HiCi] DSR 

主　　题：Best approximation Duality Haugazeau Monotone operator Primal-dual algorithm Splitting algorithm Strong convergence 

摘      要：Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of Kuhn-Tucker points of a general Hilbertian composite monotone inclusion problem. Applications to systems of coupled monotone inclusions are presented. Our framework does not impose additional assumptions on the operators present in the formulation, and it does not require knowledge of the norm of the linear operators involved in the compositions or the inversion of linear operators.