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

arXiv: https://arxiv.org/abs/1908.11835 · HTML: https://mlsanity.com/paper/1908.11835/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization](https://mlsanity.com/paper/2209.01850/) (2022)

## Abstract (arXiv)

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.