Distributed consensus-based solver for semi-definite programming: An optimization viewpoint. (September 2021)

• Record Type: Journal Article
• Authors: Li, Weijian; Zeng, Xianlin; Hong, Yiguang; Ji, Haibo
• Is Part Of: Automatica. Volume 131(2021)
• Publication Date: 2021-09
• Subjects: Distributed optimization -- Consensus-based algorithm -- Semi-definite programming -- Sparsity; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109737
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper aims at the distributed computation for semi-definite programming (SDP) problems over multi-agent networks. Two SDP problems, including a non-sparse case and a sparse case, are transformed into distributed optimization problems, respectively, by fully exploiting their structures and introducing consensus constraints. Inspired by primal–dual and consensus methods, we propose two distributed algorithms for the two cases with the help of projection and derivative feedback techniques. Furthermore, we prove that the algorithms converge to their optimal solutions, and moreover, their convergences rates are evaluated by the duality gap.