scholarly journals A Proximal Alternating Direction Method of Multiplier for Linearly Constrained Nonconvex Minimization

2020 ◽  
Vol 30 (3) ◽  
pp. 2272-2302
Author(s):  
Jiawei Zhang ◽  
Zhi-Quan Luo
Keyword(s):  
Alternating Direction Method ◽  
Nonconvex Minimization ◽  
Alternating Direction ◽  
Linearly Constrained ◽  
Proximal Alternating Direction Method

A Symmetric Alternating Direction Method of Multipliers for Separable Nonconvex Minimization Problems

2017 ◽  
Vol 34 (06) ◽  
pp. 1750030 ◽  
Author(s):  
Zhongming Wu ◽  
Min Li ◽  
David Z. W. Wang ◽  
Deren Han
Keyword(s):  
Linear Constraints ◽  
Bounded Sequence ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Penalty Parameter ◽  
Augmented Lagrangian Function ◽  
Nonconvex Minimization ◽  
Nonconvex Functions ◽  
Alternating Direction ◽  
The Given

In this paper, we propose a symmetric alternating method of multipliers for minimizing the sum of two nonconvex functions with linear constraints, which contains the classic alternating direction method of multipliers in the algorithm framework. Based on the powerful Kurdyka–Łojasiewicz property, and under some assumptions about the penalty parameter and objective function, we prove that each bounded sequence generated by the proposed method globally converges to a critical point of the augmented Lagrangian function associated with the given problem. Moreover, we report some preliminary numerical results on solving [Formula: see text] regularized sparsity optimization and nonconvex feasibility problems to indicate the feasibility and effectiveness of the proposed method.

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