An adaptive penalty-like continuous-time algorithm to constrained distributed convex optimization |
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| Institution: | 1. Faculty of Information Engineering, Guangdong University of Technology, Guangzhou, 510006, China;1. Shanghai University of Engineering Science, Shanghai, 201620, China;2. Shanghai Electric Automation Group, Shanghai, 200023, China;3. Key Laboratory of Smart Manufacturing in Energy Chemical Process (East China University of Science and Technology), Ministry of Education, Shanghai, 200237, China;1. School of Electrical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, China;2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China;3. Center for Interdisciplinary Information Science Research, Zhengzhou University, Zhengzhou 450001, China;4. School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Wollongong, NSW 2522, Australia;1. Department of Information Engineering and Mathematics, University of Siena, Siena 53100, Italy;2. Department of Information Engineering, University of Florence, via S. Marta 3, Firenze 50139, Italy;1. Electrical Engineering Department, Faculty of Engineering, Cairo university, Egypt;2. Department of Mechatronics, Faculty of Engineering, Autonomous University Carmen, Cd. del Carmen 24180, Mexico;3. Departamento de Control Automatico, CINVESTAV, A.P. 14-740, Mexico D.F. CP 07000, Mexico |
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| Abstract: | This paper considers a nonsmooth constrained distributed convex optimization over multi-agent systems. Each agent in the multi-agent system only has access to the information of its objective function and constraint, and cooperatively minimizes the global objective function, which is composed of the sum of local objective functions. A novel continuous-time algorithm is proposed to solve the distributed optimization problem and effectively characterize the appropriate gain of the penalty function. It should be noted that the proposed algorithm is based on an adaptive strategy to avoid introducing the primal-dual variables and estimating the related exact penalty parameters. Additional, it is demonstrated that the state solution of the proposed algorithm achieves consensus and converges to an optimal solution of the optimization problem. Finally, numerical simulations are given and the proposed algorithm is applied to solve the optimal placement problem and energy consumption problem. |
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