# A primal-dual method for conic constrained distributed optimization problems

arXiv: https://arxiv.org/abs/1607.02536 · HTML: https://mlsanity.com/paper/1607.02536/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2016.

## Built on by (most cited first, 4 of 4)

- [DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization](https://mlsanity.com/paper/2209.01850/) (2022)
- [Federated Learning with Convex Global and Local Constraints](https://mlsanity.com/paper/2310.10117/) (2023)
- [Federated Composite Saddle Point Optimization](https://mlsanity.com/paper/2305.15643/) (2023)
- [Federated Learning-Assisted Optimization of Mobile Transmission with Digital Twins](https://mlsanity.com/paper/2602.18627/) (2026)

## Abstract (arXiv)

We consider cooperative multi-agent consensus optimization problems over an undirected network of agents, where only those agents connected by an edge can directly communicate. The objective is to minimize the sum of agent-specific composite convex functions over agent-specific private conic constraint sets; hence, the optimal consensus decision should lie in the intersection of these private sets. We provide convergence rates both in sub-optimality, infeasibility and consensus violation; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithms; and show how to extend these methods to handle time-varying communications networks and to solve problems with resource sharing constraints.