Continuous-Time Distributed Subgradient Algorithm for Convex Optimization With General Constraints

• Published in: IEEE transactions on automatic control Vol. 64; no. 4; pp. 1694 - 1701
• Main Authors: Zhu, Yanan, Yu, Wenwu, Wen, Guanghui, Chen, Guanrong, Ren, Wei
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computational geometry; Computer simulation; Continuous-time subgradient algorithm; Convergence; Convex analysis; Convex functions; Convexity; distributed convex optimization; Hierarchies; Indexes; Linear programming; Multi-agent systems; multiagent systems; nonsmooth analysis; Optimization; Protocols; Signal processing algorithms
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2852602

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch-Kuhn-Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis.