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arXiv · 1405.6637

The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces

Miroslav Bacak·Simeon Reich
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Abstract

We study a nonlinear semigroup associated to a nonexpansive mapping on a Hadamard space and establish its weak convergence to a fixed point. A discrete-time counterpart of such a semigroup, the proximal point algorithm, turns out to have the same asymptotic behavior. This complements several results in the literature -- both classical and more recent ones. As an application, we obtain a new approach to heat flows in singular spaces for discrete, as well as continuous times.

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Miroslav Bacak, Simeon Reich. 2014-07-24. The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces. https://arxiv.org/abs/1405.6637

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