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Universal bounds for fixed point iterations via optimal transport metrics

Abstract : We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel'skii-Mann fixed point iterations for non-expansive maps. We also describe some of their very special properties, including their monotonicity and the so-called "convex quadrangle inequality" that yields a greedy algorithm to compute them efficiently.
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Preprints, Working Papers, ...
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https://hal-univ-tln.archives-ouvertes.fr/hal-03482088
Contributor : Thierry Champion Connect in order to contact the contributor
Submitted on : Wednesday, December 15, 2021 - 4:44:18 PM
Last modification on : Thursday, December 16, 2021 - 3:18:54 AM

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  • HAL Id : hal-03482088, version 1
  • ARXIV : 2108.00300

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Thierry Champion, Mario Bravo, Roberto Cominetti. Universal bounds for fixed point iterations via optimal transport metrics. 2021. ⟨hal-03482088⟩

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Metrics

Les métriques sont temporairement indisponibles