Distributed solutions of convex feasibility problems with sparsely coupled constraints
Yingying Xiao, Jianghai Hu · 2017
In this paper, distributed algorithms for solving the convex feasibility problem with sparse constraints are proposed. The proposed algorithms exploit the sparsity of the constraints to reduce the storage and communication requirements for individual agents: each agent only maintains its own variable together with its desired values for the variables of those neighboring agents whose valuations help determining its feasibility; at each iteration, each agent carries out projection and consensus operations based on information received from only the relevant neighboring agents. We show that the proposed algorithms converge asymptotically to a feasible solution starting from any initial guess and, under some further assumptions, the convergence speed is exponential. The algorithms' effectiveness is demonstrated through the simulation results on several application examples.