Continuous-time distributed optimization with strictly pseudoconvex objective functions

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 optimizati...

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Veröffentlicht in:Journal of the Franklin Institute Jg. 359; H. 2; S. 1483 - 1502
Hauptverfasser: Xu, Hang, Lu, Kaihong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elmsford Elsevier Ltd 01.01.2022
Elsevier Science Ltd
Schlagworte:
Algorithms
Computational geometry
Continuous time systems
Convex analysis
Convexity
Graph theory
Graphical representations
Multiagent systems
Optimization
Topology
ISSN:0016-0032, 1879-2693, 0016-0032
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2021.11.034