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.
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}
}