DISTRIBUTED SOLUTIONS TO COUPLED CONVEX FEASIBILITY AND OPTIMIZATION PROBLEMS ON AGENT NETWORKS

This thesis studies the distributed solutions to the coupled convex feasibility and optimization problems on agent networks, with the aim of reducing the storage and communication requirements for individual agents by exploiting the potential coupling sparsity across agents. We first focus on the convex feasibility problems. Four iterative solutions are proposed, where each agent only maintains its own variable together with its desired values for those neighboring agents whose valuations help determining its feasibility; within each iteration, projection and consensus operations are carried out by agents in parallel based on information from only the relevant neighbors. Then the approach is extended to solve convex optimization problems for a group of agents whose constraints as well as objective functions may depend on neighbors' variables. Similar solution algorithms are developed by replacing the projection with the proximal operator. Finally, we consider the optimization problems subject to global constraints that involve every agent on the network in addition to the local couplings. Distributed algorithms (with or without a coordinator) following the same approach are proposed. Convergence analysis and numerical examples are provided to demonstrate the effectiveness of the proposed algorithms.