Continuous-time distributed optimization with strictly pseudoconvex objective functions |
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| Institution: | 1. School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China;2. Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China;1. Institute for Problems of Mechanical Engineering of the Russian Academy of Sciences, 61 Bolshoy Prospekt V.O., St. Petersburg 199178, Russia;2. Gubkin University, 65 Leninsky Prospekt, Moscow 119991, Russia;1. School of Aerospace Science and Technology, Xidian University, Xi’an 710071, PR China;2. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, PR China;1. School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. School of Mathematics, Southeast University, Nanjing 210096, China |
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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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