Algorithm Implementation for Distributed Convex Intersection Computation

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.