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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| Published in | Journal of the Franklin Institute Vol. 359; no. 2; pp. 1483 - 1502 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elmsford
Elsevier Ltd
01.01.2022
Elsevier Science Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0016-0032 1879-2693 0016-0032 |
| DOI | 10.1016/j.jfranklin.2021.11.034 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Xu, Hang Lu, Kaihong |
| Author_xml | – sequence: 1 givenname: Hang surname: Xu fullname: Xu, Hang – sequence: 2 givenname: Kaihong surname: Lu fullname: Lu, Kaihong email: khong_lu@163.com |
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| CitedBy_id | crossref_primary_10_1016_j_automatica_2023_111203 crossref_primary_10_1016_j_jfranklin_2023_08_009 crossref_primary_10_1109_TNNLS_2023_3245812 crossref_primary_10_1016_j_jfranklin_2024_107002 crossref_primary_10_1016_j_jfranklin_2025_107611 crossref_primary_10_1016_j_jfranklin_2023_10_041 crossref_primary_10_1016_j_jfranklin_2023_11_017 crossref_primary_10_1007_s11768_023_00181_8 crossref_primary_10_1109_TAC_2024_3453117 crossref_primary_10_1109_TSMC_2023_3331260 |
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| SubjectTerms | Algorithms Computational geometry Continuous time systems Convex analysis Convexity Graph theory Graphical representations Multiagent systems Optimization Topology |
| Title | Continuous-time distributed optimization with strictly pseudoconvex objective functions |
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