Continuous-time distributed optimization with strictly pseudoconvex objective functions

• Published in: Journal of the Franklin Institute Vol. 359; no. 2; pp. 1483 - 1502
• Main Authors: Xu, Hang, Lu, Kaihong
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.01.2022; Elsevier Science Ltd
• Subjects: Algorithms; Computational geometry; Continuous time systems; Convex analysis; Convexity; Graph theory; Graphical representations; Multiagent systems; Optimization; Topology
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.11.034

In this paper, the distributed optimization problem is investigated by employing a continuous-time multi-agent system. The objective of agents is to cooperatively minimize the sum of local objective functions subject to a convex set. Unlike most of the existing works on distributed convex optimization, here we consider the case where the objective function is pseudoconvex. In order to solve this problem, we propose a continuous-time distributed project gradient algorithm. When running the presented algorithm, each agent uses only its own objective function and its own state information and the relative state information between itself and its adjacent agents to update its state value. The communication topology is represented by a time-varying digraph. Under mild assumptions on the graph and the objective function, it shows that the multi-agent system asymptotically reaches consensus and the consensus state is the solution to the optimization problem. Finally, several simulations are carried out to verify the correctness of our theoretical achievements.