# Multi-agent constrained optimization of a strongly convex function over time-varying directed networks

## TL;DR

This paper develops decentralized algorithms for multi-agent convex optimization over dynamic networks, providing convergence guarantees and analyzing the impact of network topology on performance.

## Contribution

It introduces new algorithms for strongly convex functions with convergence analysis over time-varying directed networks.

## Key findings

- Convergence rates are established for suboptimality, infeasibility, and consensus violation.
- Network topology significantly affects convergence speed.
- Algorithms work with non-smooth convex functions and private conic constraints.

## Abstract

We consider 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 possibly non-smooth composite convex functions over agent-specific private conic constraint sets; hence, the optimal consensus decision should lie in the intersection of these private sets. Assuming the sum function is strongly convex, we provide convergence rates in suboptimality, infeasibility and consensus violation; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithms.