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Algorithm Implementation for Distributed Convex Intersection Computation

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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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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Bingchang Wang & Xin Yu

  2. School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, 250101, China

    Dandan Pang

Authors
  1. Bingchang Wang
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  2. Xin Yu
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  3. Dandan Pang
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Corresponding author

Correspondence to Bingchang Wang.

Additional information

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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Cite this article

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

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