Distributed Proximal Algorithms for Multiagent Optimization With Coupled Inequality Constraints

• Published in: IEEE transactions on automatic control Vol. 66; no. 3; pp. 1223 - 1230
• Main Authors: Li, Xiuxian, Feng, Gang, Xie, Lihua
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accessibility; Algorithms; Convergence; Convex functions; Coupled inequality constraints; Distributed algorithms; distributed optimization; Iterative methods; Linear programming; Machine learning algorithms; Minimization; multiagent networks; Multiagent systems; Optimization; proximal point algorithm (PPA); Saddle points
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.2989282

This article aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set constraint and coupled inequality constraints whose information is only partially accessible to each agent. For this problem, a distributed proximal-based algorithm, called distributed proximal primal-dual algorithm, is proposed based on the celebrated centralized proximal point algorithm. It is shown that the proposed algorithm can lead to the global optimal solution with a general step size, which is diminishing and nonsummable, but not necessarily square summable, and the saddle-point running evaluation error vanishes proportionally to <inline-formula><tex-math notation="LaTeX">O(1/\sqrt{k})</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">k>0</tex-math></inline-formula> is the iteration number. Finally, a simulation example is presented to corroborate the effectiveness of the proposed algorithm.