Variable Metric Forward-Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function

作     者：Chouzenoux, Emilie Pesquet, Jean-Christophe Repetti, Audrey 

作者机构：Univ Paris Est Marne la Vallee Lab Informat Gaspard Monge F-77454 Champs Sur Marne Marne La Vallee France Univ Paris Est Marne la Vallee CNRS UMR 8049 F-77454 Champs Sur Marne Marne La Vallee France 

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162卷第1期

页      面：107-132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：Nonconvex optimization Nonsmooth optimization Majorize-Minimize algorithms Forward-Backward algorithm Image reconstruction Proximity operator 

摘      要：We consider the minimization of a function G defined on , which is the sum of a (not necessarily convex) differentiable function and a (not necessarily differentiable) convex function. Moreover, we assume that G satisfies the Kurdyka-Aojasiewicz property. Such a problem can be solved with the Forward-Backward algorithm. However, the latter algorithm may suffer from slow convergence. We propose an acceleration strategy based on the use of variable metrics and of the Majorize-Minimize principle. We give conditions under which the sequence generated by the resulting Variable Metric Forward-Backward algorithm converges to a critical point of G. Numerical results illustrate the performance of the proposed algorithm in an image reconstruction application.