# On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

arXiv: https://arxiv.org/abs/1303.2875 · HTML: https://mlsanity.com/paper/1303.2875/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2013.

## Built on by (most cited first, 1 of 1)

- [Accelerated nonlinear primal-dual hybrid gradient methods with applications to supervised machine learning](https://mlsanity.com/paper/2109.12222/) (2021)

## Abstract (arXiv)

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in citevu for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of O(1/n) and O(ωn), for ω ∈ (0,1), respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and support vector machines classification.