Generalized Asymmetric Forward-Backward-Adjoint Algorithms for Convex-Concave Saddle-Point Problem

作     者：Bai, Jianchao Chen, Yang Yu, Xue Zhang, Hongchao 

作者机构：Northwestern Polytech Univ Sch Math & Stat Xian 710129 Peoples R China Northwestern Polytech Univ Key Lab Complex Sci Aerosp MOE Xian 710129 Peoples R China MIIT Key Lab Dynam & Control Complex Syst Xian 710129 Peoples R China Renmin Univ China Ctr Appl Stat Sch Stat Beijing 100872 Peoples R China Beijing Adv Innovat Ctr Future Blockchain & Privac Beijing 100191 Peoples R China Louisiana State Univ Dept Math Baton Rouge LA 70803 USA 

出 版 物：《JOURNAL OF SCIENTIFIC COMPUTING》 (J Sci Comput)

年 卷 期：2025年第102卷第3期

页      面：1-33页

核心收录：

学科分类：08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China 

主　　题：Saddle-point problem Asymmetric forward-backward-adjoint algorithm Convergence and complexity Image processing 

摘      要：The convex-concave minimax problem, also known as the saddle-point problem, has been extensively studied from various aspects including the algorithm design, convergence condition and complexity. In this paper, we propose a generalized asymmetric forward-backward-adjoint algorithm (G-AFBA) to solve such a problem by utilizing both the proximal techniques and the extrapolation of primal-dual updates. Besides applying proximal primal-dual updates, G-AFBA enjoys a more relaxed convergence condition, namely, more flexible and possibly larger proximal stepsizes, which could result in significant improvements in numerical performance. We study the global convergence of G-AFBA as well as its sublinear convergence rate on both ergodic iterates and non-ergodic optimality error. The linear convergence rate of G-AFBA is also established under a calmness condition. By different ways of parameter and problem setting, we show that G-AFBA has close relationships with several well-established or new algorithms. We further propose an adaptive and a stochastic (inexact) versions of G-AFBA. Our numerical experiments on solving the robust principal component analysis problem and the 3D CT reconstruction problem indicate the efficiency of both the deterministic and stochastic versions of G-AFBA.