{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T14:33:37Z","timestamp":1724855617093},"reference-count":30,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2017,12]]},"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\u2013\u0141ojasiewicz 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. <\/jats:p>","DOI":"10.1142\/s0217595917500300","type":"journal-article","created":{"date-parts":[[2017,11,24]],"date-time":"2017-11-24T03:18:34Z","timestamp":1511493514000},"page":"1750030","source":"Crossref","is-referenced-by-count":23,"title":["A Symmetric Alternating Direction Method of Multipliers for Separable Nonconvex Minimization Problems"],"prefix":"10.1142","volume":"34","author":[{"given":"Zhongming","family":"Wu","sequence":"first","affiliation":[{"name":"School of Economics and Management, Southeast University, Nanjing 211189, P. R. China"}]},{"given":"Min","family":"Li","sequence":"additional","affiliation":[{"name":"School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China"}]},{"given":"David Z. 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