Solving Composite Fixed Point Problems with Block Updates

Advances in Nonlinear Analysis

article

Patrick L. Combettes¹  Lilian E. Glaudin² 

[1] North Carolina State University, Department of Mathematics;Université Toulouse Capitole

关键词: averaged operator;    constrained minimization;    forward-backward splitting;    fixed point iterations;    monotone operator;    nonexpansive operator;    variational inequality;   

DOI  :  10.1515/anona-2020-0173

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators that do not share common fixed points, current methods require the activation of all the operators at each iteration, and the question of maintaining convergence while updating only blocks of operators is open. We propose a method that achieves this goal and analyze its asymptotic behavior. Weak, strong, and linear convergence results are established by exploiting a connection with the theory of concentrating arrays. Applications to several nonlinear and nonsmooth analysis problems are presented, ranging from monotone inclusions and inconsistent feasibility problems, to variational inequalities and minimization problems arising in data science.

【 授权许可】

CC BY