# Distributed Difference of Convex Optimization

arXiv: https://arxiv.org/abs/2407.16728 · HTML: https://mlsanity.com/paper/2407.16728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 14 of 14)

- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [MARINA: Faster Non-Convex Distributed Learning with Compression](https://mlsanity.com/paper/2102.07845/) (2021)
- [Push-Pull Gradient Methods for Distributed Optimization in Networks](https://mlsanity.com/paper/1810.06653/) (2018)
- [On Nonconvex Decentralized Gradient Descent](https://mlsanity.com/paper/1608.05766/) (2016)
- [Distributed Nonconvex Constrained Optimization over Time-Varying Digraphs](https://mlsanity.com/paper/1809.01106/) (2018)
- [Distributed Non-Convex Optimization with Sublinear Speedup under Intermittent Client Availability](https://mlsanity.com/paper/2002.07399/) (2020)
- [A fast randomized incremental gradient method for decentralized non-convex optimization](https://mlsanity.com/paper/2011.03853/) (2020)
- [A proximal difference-of-convex algorithm with extrapolation](https://mlsanity.com/paper/1612.06265/) (2016)
- [DC approximation approaches for sparse optimization](https://mlsanity.com/paper/1407.0286/) (2014)
- [On the Pervasiveness of Difference-Convexity in Optimization and Statistics](https://mlsanity.com/paper/1704.03535/) (2017)
- [DC-DistADMM: ADMM Algorithm for Constrained Distributed Optimization over Directed Graphs](https://mlsanity.com/paper/2003.13742/) (2020)
- [Fast AC Power Flow Optimization using Difference of Convex Functions Programming](https://mlsanity.com/paper/1602.02097/) (2016)
- [Distributed finite-time termination for consensus algorithm in switching topologies](https://mlsanity.com/paper/1909.00059/) (2019)
- [Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension](https://mlsanity.com/paper/2007.13050/) (2020)

## Abstract (arXiv)

In this article, we focus on solving a class of distributed optimization problems involving n agents with the local objective function at every agent i given by the difference of two convex functions fi and gi (difference-of-convex (DC) form), where fi and gi are potentially nonsmooth. The agents communicate via a directed graph containing n nodes. We create smooth approximations of the functions fi and gi and develop a distributed algorithm utilizing the gradients of the smooth surrogates and a finite-time approximate consensus protocol. We term this algorithm as DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric directed graph topologies and can be synthesized distributively. We establish that the DDC-Consensus algorithm converges to a stationary point of the nonconvex distributed optimization problem. The performance of the DDC-Consensus algorithm is evaluated via a simulation study to solve a nonconvex DC-regularized distributed least squares problem. The numerical results corroborate the efficacy of the proposed algorithm.