# Projective Splitting with Forward Steps only Requires Continuity

arXiv: https://arxiv.org/abs/1809.07180 · HTML: https://mlsanity.com/paper/1809.07180/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2018.

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

- [Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers](https://mlsanity.com/paper/2106.13067/) (2021)

## Abstract (arXiv)

A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous. This paper shows that the Lipschitz assumption is unnecessary when the forward steps are performed in finite-dimensional spaces: a backtracking linesearch yields a convergent algorithm for operators that are merely continuous with full domain.