English

Projective Splitting with Forward Steps only Requires Continuity

Optimization and Control 2020-02-19 v1 Machine Learning Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.1809.07180,
  title  = {Projective Splitting with Forward Steps only Requires Continuity},
  author = {Patrick R. Johnstone and Jonathan Eckstein},
  journal= {arXiv preprint arXiv:1809.07180},
  year   = {2020}
}

Comments

15 pages. arXiv admin note: text overlap with arXiv:1803.07043

R2 v1 2026-06-23T04:11:34.633Z