# An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems

arXiv: https://arxiv.org/abs/1402.5291 · HTML: https://mlsanity.com/paper/1402.5291/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2014.

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

- [Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems](https://mlsanity.com/paper/2212.07844/) (2022)
- [Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developments](https://mlsanity.com/paper/2303.17192/) (2023)
- [Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuity](https://mlsanity.com/paper/2206.00973/) (2022)

## Abstract (arXiv)

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian operator. By making use of the product space approach, we expand it to the solving of inclusion problems involving mixtures of linearly composed and parallel-sum type monotone operators. We obtain in this way an inertial forward-backward-forward primal-dual splitting algorithm having as main characteristic the fact that in the iterative scheme all operators are accessed separately either via forward or via backward evaluations. We present also the variational case when one is interested in the solving of a primal-dual pair of convex optimization problems with intricate objective functions.