The forward-backward algorithm and the normal problem

Walaa M. Moursi

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arXiv · 1608.02240

The forward-backward algorithm and the normal problem

Walaa M. Moursi

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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.

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Walaa M. Moursi. 2016-08-07. The forward-backward algorithm and the normal problem. https://arxiv.org/abs/1608.02240

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