# Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization

arXiv: https://arxiv.org/abs/2302.03238 · HTML: https://mlsanity.com/paper/2302.03238/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 20 of 20)

- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [On the Linear Convergence of the ADMM in Decentralized Consensus Optimization](https://mlsanity.com/paper/1307.5561/) (2013)
- [A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates](https://mlsanity.com/paper/1704.07807/) (2017)
- [Exact Diffusion for Distributed Optimization and Learning --- Part I: Algorithm Development](https://mlsanity.com/paper/1702.05122/) (2017)
- [Decentralized Proximal Gradient Algorithms with Linear Convergence Rates](https://mlsanity.com/paper/1909.06479/) (2019)
- [Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists](https://mlsanity.com/paper/1912.00137/) (2019)
- [Distributed Algorithms for Composite Optimization: Unified Framework and Convergence Analysis](https://mlsanity.com/paper/2002.11534/) (2020)
- [Distributed Linearized Alternating Direction Method of Multipliers for Composite Convex Consensus Optimization](https://mlsanity.com/paper/1512.08122/) (2015)
- [A new primal-dual algorithm for minimizing the sum of three functions with a linear operator](https://mlsanity.com/paper/1611.09805/) (2016)
- [Asymmetric Forward-Backward-Adjoint Splitting for Solving Monotone Inclusions Involving Three Operators](https://mlsanity.com/paper/1602.08729/) (2016)
- [Geometrically Convergent Distributed Optimization with Uncoordinated Step-Sizes](https://mlsanity.com/paper/1609.05877/) (2016)
- [Distributed Discrete-time Optimization in Multi-agent Networks Using only Sign of Relative State](https://mlsanity.com/paper/1709.08360/) (2017)
- [Decomposing Linearly Constrained Nonconvex Problems by a Proximal Primal Dual Approach: Algorithms, Convergence, and Applications](https://mlsanity.com/paper/1604.00543/) (2016)
- [Accelerated first-order primal-dual proximal methods for linearly constrained composite convex programming](https://mlsanity.com/paper/1606.09155/) (2016)
- [IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method](https://mlsanity.com/paper/2006.06733/) (2020)
- [On the Equivalence of Inexact Proximal ALM and ADMM for a Class of Convex Composite Programming](https://mlsanity.com/paper/1803.10803/) (2018)
- [On construction of splitting contraction algorithms in a prediction-correction framework for separable convex optimization](https://mlsanity.com/paper/2204.11522/) (2022)

## Built on by (most cited first, 5 of 5)

- [FedCanon: Non-Convex Composite Federated Learning with Efficient Proximal Operation on Heterogeneous Data](https://mlsanity.com/paper/2504.11903/) (2025)
- [A Proximal Gradient Method With Probabilistic Multi-Gossip Communications for Decentralized Composite Optimization](https://mlsanity.com/paper/2312.11861/) (2023)
- [Achieving Linear Speedup with ProxSkip in Distributed Stochastic Optimization](https://mlsanity.com/paper/2310.07983/) (2023)
- [Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration](https://mlsanity.com/paper/2602.16148/) (2026)
- [Adaptive Decentralized Composite Optimization via Three-Operator Splitting](https://mlsanity.com/paper/2602.17545/) (2026)

## Abstract (arXiv)

This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and nonsmooth terms. The proposed algorithm uses uncoordinated network-independent constant stepsizes and only needs to approximately solve a sequence of proximal mappings, which is advantageous for solving decentralized composite optimization problems where the proximal mappings of the nonsmooth loss functions may not have analytical solutions. For the general convex case, we prove an O(1/k) convergence rate of the proposed algorithm, which can be improved to o(1/k) if the proximal mappings are solved exactly. Furthermore, with metric subregularity, we establish a linear convergence rate for the proposed algorithm. Numerical experiments demonstrate the efficiency of the algorithm.