Abstract
Intersection computation of convex sets is a typical problem in distributed optimization. In this paper, the algorithm implementation is investigated for distributed convex intersection computation problems. In a multi-agent network, each agent is associated with a convex set. The objective is for all the agents to achieve an agreement within the intersection of the associated convex sets. A distributed “projected consensus algorithm” is employed, and the computation of the projection term is converted to a constrained optimization problem. The solution of the optimization problem is determined by Karush-Kuhn-Tucker (KKT) conditions. Some implementable algorithms based on the simplex method are introduced to solve the optimization problem. Two numerical examples are given to illustrate the effectiveness of the algorithms.
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This work was supported by the National Natural Science Foundation of China under Grant Nos. 61773241 and 61503218.
This paper was recommended for publication by Editor HONG Yiguang.
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Wang, B., Yu, X. & Pang, D. Algorithm Implementation for Distributed Convex Intersection Computation. J Syst Sci Complex 33, 15–25 (2020). https://doi.org/10.1007/s11424-019-8161-9
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DOI: https://doi.org/10.1007/s11424-019-8161-9