A Fully Parallel Distributed Algorithm for Nonsmooth Convex Optimization With Coupled Constraints: Applications to Distributed Consensus-Based Optimization and Distributed Resource Allocation
Seyyed Shaho Alaviani, Atul G. Kelkar, Umesh Vaidya · IEEE Transactions on Automatic Control · 2025
This paper 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-timefully paralleldistributedalgorithm is thefirstof its kind in the sense that it does not require diminishing step size, (sub)gradient, and/or solving a sub-problem at each time step. The algorithm is able to converge to anoptimalsolution foranylocal convex cost functions (without differentiability or Lipschitz continuity) andanylocal convex constraint sets (compact or unbounded) of agents witharbitraryinitialization overanyundirected static (non-switching) networks in synchronous protocol. Important applications of the problem can be distributed consensus-based optimization and distributed resource allocation. Thetechniqueutilized 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.