Distributed Design for Nuclear Norm Minimization of Linear Matrix Equations With Constraints

• 成果类型: Article
• 署名作者: Li, Weijian; Zeng, Xianlin; Hong, Yiguang; Ji, Haibo
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2981930
• 发表日期: 2021
• 页码: 745-752
• 关键词: Distributed matrix computation; distributed optimization; linear equality constraints; nuclear norm minimization

摘要

This article aims at a distributed design to minimize the nuclear norm (the sum of all singular values) under linear equality constraints over a multiagent network. The problem is reformulated as a distributed trace norm minimization problem by introducing substitutional variables. A distributed projected primal-dual algorithm is proposed for the reformulation. It is shown that the algorithm converges to an optimal solution with a rate of O(1/t). Numerical simulations on three classical problems, including linear matrix equality constraints, cardinality minimization, and low-rank matrix completion, are carried out for illustration.