Convergence of Generalized Alternating Direction Method of Multipliers for Nonseparable Nonconvex Objective with Linear Constraints  

作　　者：Ke GUO Xin WANG 

机构地区：[1]School of Mathematics and Information, China West Normal University

出　　处：《Journal of Mathematical Research with Applications》2018年第5期523-540,共18页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11571178;11801455);the Fundamental Research Funds of China West Normal University(Grant No.17E084)

摘　　要：In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functions. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality, we prove that the sequence generated by the GADMM converges to a critical point of the augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Moreover, we also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functions. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality, we prove that the sequence generated by the GADMM converges to a critical point of the augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Moreover, we also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.

关 键 词：generalized alternating direction method of multipliers Kurdyka Lojasiewicz in-equality nonconvex optimization 

分 类 号：O224[理学—运筹学与控制论]