Continuous-Time Distributed Subgradient Algorithm for Convex Optimization With General Constraints

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch-Kuhn-Tucker condition...

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Published in:	IEEE transactions on automatic control Vol. 64; no. 4; pp. 1694 - 1701
Main Authors:	Zhu, Yanan, Yu, Wenwu, Wen, Guanghui, Chen, Guanrong, Ren, Wei
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.04.2019 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Computational geometry Computer simulation Continuous-time subgradient algorithm Convergence Convex analysis Convex functions Convexity distributed convex optimization Hierarchies Indexes Linear programming Multi-agent systems multiagent systems nonsmooth analysis Optimization Protocols Signal processing algorithms
ISSN:	0018-9286, 1558-2523
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Abstract	The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch-Kuhn-Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis.
AbstractList	The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch–Kuhn–Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis.
Author	Zhu, Yanan Ren, Wei Yu, Wenwu Wen, Guanghui Chen, Guanrong
Author_xml	– sequence: 1 givenname: Yanan orcidid: 0000-0001-7980-6282 surname: Zhu fullname: Zhu, Yanan email: zhuxiaoyazhuyanan@163.com organization: School of Mathematics, Southeast University, Nanjing, China – sequence: 2 givenname: Wenwu orcidid: 0000-0003-3755-179X surname: Yu fullname: Yu, Wenwu email: wwyu@seu.edu.cn organization: School of Mathematics, Southeast University, Nanjing, China – sequence: 3 givenname: Guanghui orcidid: 0000-0003-0070-8597 surname: Wen fullname: Wen, Guanghui email: wenguanghui@gmail.com organization: School of Mathematics, Southeast University, Nanjing, China – sequence: 4 givenname: Guanrong orcidid: 0000-0003-1381-7418 surname: Chen fullname: Chen, Guanrong email: eegchen@cityu.edu.hk organization: Department of Electronic Engineering, City University of Hong Kong, Hong Kong – sequence: 5 givenname: Wei orcidid: 0000-0002-2818-9752 surname: Ren fullname: Ren, Wei email: ren@ee.ucr.edu organization: Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
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SubjectTerms	Algorithms Computational geometry Computer simulation Continuous-time subgradient algorithm Convergence Convex analysis Convex functions Convexity distributed convex optimization Hierarchies Indexes Linear programming Multi-agent systems multiagent systems nonsmooth analysis Optimization Protocols Signal processing algorithms
Title	Continuous-Time Distributed Subgradient Algorithm for Convex Optimization With General Constraints
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