English

The forward-backward algorithm and the normal problem

Optimization and Control 2016-08-09 v1 Numerical Analysis

Abstract

The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory.

Keywords

Cite

@article{arxiv.1608.02240,
  title  = {The forward-backward algorithm and the normal problem},
  author = {Walaa M. Moursi},
  journal= {arXiv preprint arXiv:1608.02240},
  year   = {2016}
}
R2 v1 2026-06-22T15:14:20.218Z