# Inertial Douglas-Rachford splitting for monotone inclusion problems

arXiv: https://arxiv.org/abs/1403.3330 · HTML: https://mlsanity.com/paper/1403.3330/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2014.

## Built on by (most cited first, 3 of 3)

- [Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions](https://mlsanity.com/paper/2110.08150/) (2021)
- [Robust Graph Representation Learning for Local Corruption Recovery](https://mlsanity.com/paper/2202.04936/) (2022)
- [Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems](https://mlsanity.com/paper/2212.07844/) (2022)

## Abstract (arXiv)

We propose an inertial Douglas-Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the inertial version of the Krasnosel'skiui--Mann algorithm for approximating the set of fixed points of a nonexpansive operator, for which we also provide an exhaustive convergence analysis. By using a product space approach we employ these results to the solving of monotone inclusion problems involving linearly composed and parallel-sum type operators and provide in this way iterative schemes where each of the maximally monotone mappings is accessed separately via its resolvent. We consider also the special instance of solving a primal-dual pair of nonsmooth convex optimization problems and illustrate the theoretical results via some numerical experiments in clustering and location theory.