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• W2956044183 abstract "This paper studies a proximal alternating direction method of multipliers (ADMM) with variable metric indefinite proximal terms for linearly constrained convex optimization problems. The proximal ADMM plays an important role in many application areas, since the subproblems of the method are easy to solve. Recently, it is reported that the proximal ADMM with a certain fixed indefinite proximal term is faster than that with a positive semidefinite term, and still has the global convergence property. On the other hand, Gu and Yamashita studied a variable metric semidefinite proximal ADMM whose proximal term is generated by the BFGS update. They reported that a slightly indefinite matrix also makes the algorithm work well in their numerical experiments. Motivated by this fact, we consider a variable metric indefinite proximal ADMM, and give sufficient conditions on the proximal terms for the global convergence. Moreover, we propose a new indefinite proximal term based on the BFGS update which can satisfy the conditions for the global convergence." @default.
• W2956044183 created "2019-07-12" @default.
• W2956044183 creator A5041511323 @default.
• W2956044183 creator A5056828396 @default.
• W2956044183 date "2019-06-28" @default.
• W2956044183 modified "2023-09-26" @default.
• W2956044183 title "Alternating Direction Method of Multipliers with Variable Metric Indefinite Proximal Terms for Convex Optimization" @default.
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• W2956044183 doi "https://doi.org/10.48550/arxiv.1906.12112" @default.
• W2956044183 hasPublicationYear "2019" @default.
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