# Distributed Proximal Algorithms for Multi-Agent Optimization with Coupled Inequality Constraints

arXiv: https://arxiv.org/abs/1907.03245 · HTML: https://mlsanity.com/paper/1907.03245/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization](https://mlsanity.com/paper/2111.03820/) (2021)
- [Estimation Network Design framework for efficient distributed optimization](https://mlsanity.com/paper/2404.15273/) (2024)

## Abstract (arXiv)

This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set constraint and coupled inequality constraints whose information is only partially accessible to each agent. For this problem, a distributed proximal-based algorithm, called distributed proximal primal-dual (DPPD) algorithm, is proposed based on the celebrated centralized proximal point algorithm. It is shown that the proposed algorithm can lead to the global optimal solution with a general stepsize, which is diminishing and non-summable, but not necessarily square-summable, and the saddle-point running evaluation error vanishes proportionally to O(1/√k), where k>0 is the iteration number. Finally, a simulation example is presented to corroborate the effectiveness of the proposed algorithm.