Distributed quasi-monotone subgradient algorithm for nonsmooth convex optimization over directed graphs
Distributed optimization is of essential importance in networked systems. Most of the existing distributed algorithms either assume the information exchange over undirected graphs, or require that the underlying directed network topology provides a doubly stochastic weight matrix to the agents. In t...
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| Veröffentlicht in: | Automatica (Oxford) Jg. 101; S. 175 - 181 |
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| Sprache: | Englisch |
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01.03.2019
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| Abstract | Distributed optimization is of essential importance in networked systems. Most of the existing distributed algorithms either assume the information exchange over undirected graphs, or require that the underlying directed network topology provides a doubly stochastic weight matrix to the agents. In this brief paper, a distributed subgradient-based algorithm is proposed to solve nonsmooth convex optimization problems. The algorithm applies to directed graphs without using a doubly stochastic weight matrix. Moreover, the algorithm is a distributed generalization and improvement of the quasi-monotone subgradient algorithm. An O(1∕k) convergence rate is achieved. The effectiveness of our algorithm is also illustrated by a numerical example. |
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| AbstractList | Distributed optimization is of essential importance in networked systems. Most of the existing distributed algorithms either assume the information exchange over undirected graphs, or require that the underlying directed network topology provides a doubly stochastic weight matrix to the agents. In this brief paper, a distributed subgradient-based algorithm is proposed to solve nonsmooth convex optimization problems. The algorithm applies to directed graphs without using a doubly stochastic weight matrix. Moreover, the algorithm is a distributed generalization and improvement of the quasi-monotone subgradient algorithm. An O(1∕k) convergence rate is achieved. The effectiveness of our algorithm is also illustrated by a numerical example. |
| Author | Liang, Shu Wang, Leyi Yin, George |
| Author_xml | – sequence: 1 givenname: Shu surname: Liang fullname: Liang, Shu email: sliang@amss.ac.cn, sliang@ustb.edu.cn organization: Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China – sequence: 2 givenname: Leyi surname: Wang fullname: Wang, Leyi email: lywang@wayne.edu organization: Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, USA – sequence: 3 givenname: George surname: Yin fullname: Yin, George email: gyin@math.wayne.edu organization: Department of Mathematics, Wayne State University, Detroit, MI 48202, USA |
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| Cites_doi | 10.3166/EJC.18.539-557 10.1109/TAC.2014.2364096 10.1109/TAC.2012.2219953 10.1109/TAC.2014.2308612 10.1109/TAC.2013.2278132 10.1287/opre.18.1.87 10.1109/TAC.2010.2041686 10.1007/s10957-014-0677-5 10.1109/TAC.2017.2752001 10.1109/TSMCB.2011.2160394 10.1007/s10107-007-0149-x 10.1109/TAC.2008.2009515 10.1109/TAC.2016.2628807 10.1109/TAC.2016.2615066 10.1016/j.automatica.2012.08.003 10.1109/TAC.2011.2161027 10.1109/TNNLS.2016.2549566 10.1109/TAC.2011.2167817 10.1007/s10957-010-9737-7 |
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| Keywords | Quasi-monotone subgradient algorithm Distributed optimization Nonsmooth convex optimization Directed graph |
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| Title | Distributed quasi-monotone subgradient algorithm for nonsmooth convex optimization over directed graphs |
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