Title | ||
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Distributed consensus-based multi-agent convex optimization via gradient tracking technique |
Abstract | ||
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This paper considers solving a class of optimization problems over a network of agents, in which the cost function is expressed as the sum of individual objectives of the agents. The underlying communication graph is assumed to be undirected and connected. A distributed algorithm in which agents employ time-varying and heterogeneous step-sizes is proposed by combining consensus of multi-agent systems with gradient tracking technique. The algorithm not only drives the agents’ iterates to a global and consensual minimizer but also finds the optimal value of the cost function. When the individual objectives are convex and smooth, we prove that the algorithm converges at a rate of O(1/t) if the homogeneous step-size does not exceed some upper bound, and it accelerates to O(1/t) if the homogeneous step-size is sufficiently small. When at least one of the individual objectives is strongly convex and all are smooth, we prove that the algorithm converges at a linear rate of O(λt) with 0 < λ < 1 even though the step-sizes are time-varying and heterogeneous. Two numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate the theoretical findings. |
Year | DOI | Venue |
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2019 | 10.1016/j.jfranklin.2019.01.050 | Journal of the Franklin Institute |
Field | DocType | Volume |
Consensus,Mathematical optimization,Upper and lower bounds,Regular polygon,Distributed algorithm,Convex function,Iterated function,Convex optimization,Optimization problem,Mathematics | Journal | 356 |
Issue | ISSN | Citations |
6 | 0016-0032 | 1 |
PageRank | References | Authors |
0.35 | 0 | 5 |
Name | Order | Citations | PageRank |
---|---|---|---|
Huaqing Li | 1 | 534 | 34.13 |
Hao Zhang | 2 | 203 | 64.03 |
Zheng Wang | 3 | 72 | 47.08 |
Yifan Zhu | 4 | 1 | 0.35 |
Qi Han | 5 | 139 | 30.38 |