Distributed Continuous-Time Nonsmooth Convex Optimization With Coupled Inequality Constraints

• Published in: IEEE transactions on control of network systems Vol. 7; no. 1; pp. 74 - 84
• Main Authors: Li, Xiuxian, Xie, Lihua, Hong, Yiguang
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.03.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computational geometry; Computer simulation; Continuous-time algorithms; Control systems; Convex analysis; Convex functions; Convexity; coupled inequality constraints; distributed convex optimization; Eigenvalues and eigenfunctions; Heuristic algorithms; Liapunov functions; Linear programming; multiagent networks; Multiagent systems; Nonlinear programming; nonsmooth analysis; Optimization
• ISSN: 2325-5870; 2372-2533
• DOI: 10.1109/TCNS.2019.2915626

This paper studies distributed convex optimization problems over continuous-time multiagent networks subject to two types of constraints, i.e., local feasible set constraints and coupled inequality constraints, where all involved functions are not necessarily differentiable, only assumed to be convex. In order to solve this problem, a modified primal-dual continuous-time algorithm is proposed by projections on local feasible sets. With the aid of constructing a proper Lyapunov function candidate, the existence of solutions of the algorithm in the Carathéodory sense and the convergence of the algorithm to an optimal solution for the distributed optimization problem are established. Additionally, a sufficient condition is provided for making the algorithm fully distributed. Finally, the theoretical result is corroborated by a simulation example.