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.

中文翻译：

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分布凸相交计算的算法实现

凸集的相交计算是分布式优化中的典型问题。本文研究了分布式凸交点计算问题的算法实现。在多主体网络中，每个主体与一个凸集相关联。目的是让所有代理在关联凸集的交集内达成一致。采用分布式“投影共识算法”，并将投影项的计算转换为约束优化问题。优化问题的解决方案由Karush-Kuhn-Tucker（KKT）条件确定。介绍了一些基于单纯形法的可实现算法来解决优化问题。给出两个数值例子来说明算法的有效性。