A Fully Parallel Distributed Algorithm for Nonsmooth Convex Optimization With Coupled Constraints: Applications to Distributed Consensus-Based Optimization and Distributed Resource Allocation

This article aims at collaborative optimization of sum of convex functions over networks subject to globally coupled affine equality and inequality constraints whose partial information is known by each agent. The proposed discrete-time fully parallel distributed algorithm is the first of its kind in the sense that it does not require diminishing step size, (sub)gradient, and/or solving a subproblem at each time step. The algorithm is able to converge to an optimal solution for any local convex cost functions (without differentiability or Lipschitz continuity) and any local convex constraint sets (compact or unbounded) of agents with arbitrary initialization over any undirected static (nonswitching) networks in synchronous protocol. Important applications of the problem can be distributed consensus-based optimization and distributed resource allocation. The technique utilized here serves as a motivation and guidance for developing several other fully parallel distributed algorithms. Finally, a numerical example of distributed economic dispatch in power systems is provided to demonstrate the efficacy of the results.