A Decentralized Primal-dual Method for Constrained Minimization of a Strongly Convex Function
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.
Cite
@article{arxiv.1908.11835,
title = {A Decentralized Primal-dual Method for Constrained Minimization of a Strongly Convex Function},
author = {Erfan Yazdandoost Hamedani and Necdet Serhat Aybat},
journal= {arXiv preprint arXiv:1908.11835},
year = {2022}
}
Comments
A preliminary result of this paper was presented in arXiv:1706.07907 by Hamedani and Aybat. In this paper, we generalize our results to the setting where agent-specific constraints are defined by nonlinear functions rather than linear ones which greatly improves the modeling capability. This generalization requires a more complicated analysis which is studied in this separate arXiv submission