Distributed Algorithm Over Time-Varying Unbalanced Topologies for Optimization Problem Subject to Multiple Local Constraints

TL;DR

This paper introduces a novel distributed algorithm for convex optimization over dynamic, unbalanced directed networks, ensuring convergence to the optimal solution using only local information and computations.

Contribution

A new distributed discrete-time algorithm is developed for time-varying unbalanced topologies, with proven convergence and convergence rate analysis.

Findings

Algorithm converges to the optimal solution.

Convergence rate is established under mild assumptions.

Numerical simulations verify theoretical results.

Abstract

This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a distributed manner over time-varying unbalanced directed topologies by using only local information and performing only local computations. Towards this end, a new distributed discrete-time algorithm is developed by synthesizing the row stochastic matrices sequence and column stochastic matrices sequence analysis technique. Furthermore, for the developed distributed discrete-time algorithm, its convergence property to the optimal solution as well as its convergence rate are established under some mild assumptions. Numerical simulations are finally presented to verify the theoretical results.