Exponential convergence of distributed primal–dual convex optimization algorithm without strong convexity
This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map...
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| Veröffentlicht in: | Automatica (Oxford) Jg. 105; S. 298 - 306 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.07.2019
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| ISSN: | 0005-1098, 1873-2836 |
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| Abstract | This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler’s approximation method. |
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| AbstractList | This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler’s approximation method. |
| Author | Wang, Le Yi Liang, Shu Yin, George |
| Author_xml | – sequence: 1 givenname: Shu surname: Liang fullname: Liang, Shu email: 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: Le Yi surname: Wang fullname: Wang, Le Yi 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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| Keywords | Exponential convergence Metric subregularity Variational analysis Distributed optimization Convex optimization without strong convexity Rate of convergence Primal–dual algorithm |
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| SubjectTerms | Convex optimization without strong convexity Distributed optimization Exponential convergence Metric subregularity Primal–dual algorithm Rate of convergence Variational analysis |
| Title | Exponential convergence of distributed primal–dual convex optimization algorithm without strong convexity |
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