arXiv:1608.02240 Abstract | arXiv Analytics

arXiv:1608.02240 [math.OC]Abstract References Reviews Resources

The forward-backward algorithm and the normal problem

Published 2016-08-07Version 1

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.

Categories: math.OC, math.NA

Subjects: 47H09, 49M27, 65K10, 47H05, 47H14, 49M29, 49N19

Keywords: normal problem, forward-backward algorithm, forward-backward operator, examples illustrate, popular method

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