# Distributed Nonconvex Constrained Optimization over Time-Varying Digraphs

arXiv: https://arxiv.org/abs/1809.01106 · HTML: https://mlsanity.com/paper/1809.01106/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2018.

## Built on by (most cited first, 23 of 23)

- [Exponential Graph is Provably Efficient for Decentralized Deep Training](https://mlsanity.com/paper/2110.13363/) (2021)
- [On the Performance of Gradient Tracking with Local Updates](https://mlsanity.com/paper/2210.04757/) (2022)
- [Finite-Bit Quantization For Distributed Algorithms With Linear Convergence](https://mlsanity.com/paper/2107.11304/) (2021)
- [Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization](https://mlsanity.com/paper/2104.02596/) (2021)
- [Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function](https://mlsanity.com/paper/2112.14949/) (2021)
- [Decentralized Composite Optimization with Compression](https://mlsanity.com/paper/2108.04448/) (2021)
- [Hierarchical Federated Learning with Multi-Timescale Gradient Correction](https://mlsanity.com/paper/2409.18448/) (2024)
- [Decentralized gradient descent maximization method for composite nonconvex strongly-concave minimax problems](https://mlsanity.com/paper/2304.02441/) (2023)
- [PRECISION: Decentralized Constrained Min-Max Learning with Low Communication and Sample Complexities](https://mlsanity.com/paper/2303.02532/) (2023)
- [A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization](https://mlsanity.com/paper/2302.09766/) (2023)
- [DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks](https://mlsanity.com/paper/2511.12836/) (2025)
- [Variance-reduced accelerated methods for decentralized stochastic double-regularized nonconvex strongly-concave minimax problems](https://mlsanity.com/paper/2307.07113/) (2023)
- [Locally Differentially Private Gradient Tracking for Distributed Online Learning over Directed Graphs](https://mlsanity.com/paper/2310.16105/) (2023)
- [Communication-Efficient Federated Optimization over Semi-Decentralized Networks](https://mlsanity.com/paper/2311.18787/) (2023)
- [Decentralized Riemannian natural gradient methods with Kronecker-product approximations](https://mlsanity.com/paper/2303.09611/) (2023)
- [Optimized Gradient Tracking for Decentralized Online Learning](https://mlsanity.com/paper/2306.06375/) (2023)
- [Lower Bounds and Optimal Algorithms for Non-Smooth Convex Decentralized Optimization over Time-Varying Networks](https://mlsanity.com/paper/2405.18031/) (2024)
- [Exploiting Similarity for Computation and Communication-Efficient Decentralized Optimization](https://mlsanity.com/paper/2506.05791/) (2025)
- [Distributed gradient-based optimization in the presence of dependent aperiodic communication](https://mlsanity.com/paper/2201.11343/) (2022)
- [Distributed Difference of Convex Optimization](https://mlsanity.com/paper/2407.16728/) (2024)
- [An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems](https://mlsanity.com/paper/2507.22311/) (2025)
- [Provably Convergent Decentralized Optimization over Directed Graphs under Generalized Smoothness](https://mlsanity.com/paper/2601.03566/) (2026)
- [Decentralized Non-convex Stochastic Optimization with Heterogeneous Variance](https://mlsanity.com/paper/2602.11789/) (2026)

## Abstract (arXiv)

This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first algorithmic framework for the minimization of the sum of a smooth nonconvex (nonseparable) function--the agent's sum-utility--plus a Difference-of-Convex (DC) function (with nonsmooth convex part). This general formulation arises in many applications, from statistical machine learning to engineering. The proposed distributed method combines successive convex approximation techniques with a judiciously designed perturbed push-sum consensus mechanism that aims to track locally the gradient of the (smooth part of the) sum-utility. Sublinear convergence rate is proved when a fixed step-size (possibly different among the agents) is employed whereas asymptotic convergence to stationary solutions is proved using a diminishing step-size. Numerical results show that our algorithms compare favorably with current schemes on both convex and nonconvex problems.