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Universal bounds for fixed point iterations via optimal transport metrics

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Mario Bravo
  • Function : Author
Roberto Cominetti
  • Function : Author

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.

Dates and versions

hal-03482088 , version 1 (15-12-2021)

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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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