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

Zhongming Wu (), Min Li (), David Z. W. Wang () and Deren Han
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Zhongming Wu: School of Economics and Management, Southeast University, Nanjing 211189, P. R. China
Min Li: School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China
David Z. W. Wang: School of Civil and Environmental Engineering, Nanyang Technological University, Singapore
Deren Han: School of Mathematical Sciences, Jiangsu Key Labratory for NSLSCS, Nanjing Normal University, Nanjing 210023, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2017, vol. 34, issue 06, 1-27

Abstract: 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 l1/2 regularized sparsity optimization and nonconvex feasibility problems to indicate the feasibility and effectiveness of the proposed method.

Keywords: Alternating direction method of multipliers; symmetric; Kurdyka–Łojasiewicz property; nonconvex optimization; linear constraints (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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DOI: 10.1142/S0217595917500300

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