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Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets
Applied and Computational Mathematics
Volume 5, Issue 3, June 2016, Pages: 150-159
Received: Jun. 12, 2016; Accepted: Jun. 20, 2016; Published: Jul. 13, 2016
Authors
Qingguo Lü, College of Electronic and Information Engineering, Southwest University, Chongqing, PR China
Huaqing Li, College of Electronic and Information Engineering, Southwest University, Chongqing, PR China; State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, PR China
Li Xiao, Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing, PR China
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Abstract
This paper considers a distributed constrained optimization problem, where the objective function is the sum of local objective functions of distributed nodes in a network. The estimate of each agent is restricted to different convex sets. To solve this optimization problem which is not necessarily smooth, we study a novel distributed projected subgradient algorithm for multi-agent optimization with nonidentical constraint sets and switching topologies. The algorithm shows that each agent minimizes its own objective function while communicating information locally with other agents over a network with time-varying topologies but satisfying a standard connectivity property. Under the assumption that the network topology is weight-balanced, the novel distributed subgradient algorithm we proposed is proven to be convergent. Particularly, we suppose the step-size is various, which is different from previous work on multi-agent optimization that makes worst-case assumption with constant step-size.
Keywords
Distributed Optimization, Subgradient Algorithm, Multi-agent Network, Weight-Balanced
Qingguo Lü, Huaqing Li, Li Xiao, Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets, Applied and Computational Mathematics. Vol. 5, No. 3, 2016, pp. 150-159. doi: 10.11648/j.acm.20160503.19
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