Convergence of Generalized Alternating Direction Method of Multipliers for Nonseparable Nonconvex Objective with Linear Constraints
Received:September 03, 2017  Revised:June 05, 2018
Key Word: generalized alternating direction method of multipliers   Kurdyka-{\L}ojasiewicz inequality   nonconvex optimization  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11571178; 11801455) and the Fundamental Research Funds of China West Normal University (Grant No.17E084).
Author NameAffiliation
Ke GUO School of Mathematics and Information, China West Normal University, Sichuan 637002, P. R. China 
Xin WANG School of Mathematics and Information, China West Normal University, Sichuan 637002, P. R. China 
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Abstract:
      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-{\L}ojasiewicz 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.
Citation:
DOI:10.3770/j.issn:2095-2651.2018.05.010
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