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The forward-backward algorithm and the normal problem

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.

preprint2016arXivOpen access
Walaa M. Moursi
math.OCmath.NA
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Walaa M. Moursi

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