A Decentralized Primal-dual Method for Constrained Minimization of a Strongly Convex Function

TL;DR

This paper introduces a decentralized primal-dual algorithm for cooperative multi-agent optimization with constraints, achieving convergence guarantees over dynamic networks, and analyzing the impact of network topology.

Contribution

It presents a novel decentralized primal-dual method for constrained convex optimization in multi-agent systems with convergence analysis.

Findings

Convergence rates depend on network topology.

Method works over static and time-varying networks.

Achieves sublinear convergence under strong convexity.

Abstract

We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific convex functions over conic constraint sets defined by agent-specific nonlinear functions; hence, the optimal consensus decision should lie in the intersection of these private sets. Under the strong convexity assumption, we provide convergence rates for sub-optimality, infeasibility, and consensus violation in terms of the number of communications required; examine the effect of underlying network topology on the convergence rates.