# DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization

arXiv: https://arxiv.org/abs/2209.01850 · HTML: https://mlsanity.com/paper/2209.01850/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 74 references that are in the map.
- First posted on arXiv 5 Sep 2022.

## Builds on (most cited first, 25 of 25)

- [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)
- [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)
- [Push-Pull Gradient Methods for Distributed Optimization in Networks](https://mlsanity.com/paper/1810.06653/) (2018)
- [A Three-Operator Splitting Scheme and its Optimization Applications](https://mlsanity.com/paper/1504.01032/) (2015)
- [Multi-Agent Distributed Optimization via Inexact Consensus ADMM](https://mlsanity.com/paper/1402.6065/) (2014)
- [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 Randomized Block-Coordinate Primal-Dual Proximal Algorithm for Distributed Optimization](https://mlsanity.com/paper/1706.02882/) (2017)
- [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)
- [Accelerated first-order primal-dual proximal methods for linearly constrained composite convex programming](https://mlsanity.com/paper/1606.09155/) (2016)
- [Acceleration of Primal-Dual Methods by Preconditioning and Simple Subproblem Procedures](https://mlsanity.com/paper/1811.08937/) (2018)
- [On the Equivalence of Inexact Proximal ALM and ADMM for a Class of Convex Composite Programming](https://mlsanity.com/paper/1803.10803/) (2018)
- [Dualize, Split, Randomize: Toward Fast Nonsmooth Optimization Algorithms](https://mlsanity.com/paper/2004.02635/) (2020)
- [A primal-dual fixed-point algorithm for minimization of the sum of three convex separable functions](https://mlsanity.com/paper/1512.09235/) (2015)
- [A primal-dual method for conic constrained distributed optimization problems](https://mlsanity.com/paper/1607.02536/) (2016)
- [A Unifying Approximate Method of Multipliers for Distributed Composite Optimization](https://mlsanity.com/paper/2009.12732/) (2020)
- [A Decentralized Primal-dual Method for Constrained Minimization of a Strongly Convex Function](https://mlsanity.com/paper/1908.11835/) (2019)

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

- [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)
- [Decentralized Optimization with Topology-Independent Communication](https://mlsanity.com/paper/2509.14488/) (2025)
- [BALPA: A Balanced Primal-Dual Algorithm for Nonsmooth Optimization with Application to Distributed Optimization](https://mlsanity.com/paper/2212.02835/) (2022)
- [Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration](https://mlsanity.com/paper/2602.16148/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel Dual Inexact Splitting Algorithm (DISA) for distributed convex composite optimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed with a linear mapping. DISA, for the first time, eliminates the dependence of the convergent step-size range on the Euclidean norm of the linear mapping, while inheriting the advantages of the classic Primal-Dual Proximal Splitting Algorithm (PD-PSA): simple structure and easy implementation. This indicates that DISA can be executed without prior knowledge of the norm, and tiny step-sizes can be avoided when the norm is large. Additionally, we prove sublinear and linear convergence rates of DISA under general convexity and metric subregularity, respectively. Moreover, we provide a variant of DISA with approximate proximal mapping and prove its global convergence and sublinear convergence rate. Numerical experiments corroborate our theoretical analyses and demonstrate a significant acceleration of DISA compared to existing PD-PSAs.