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Journal Articles SIAM Journal on Optimization Year : 2022

On the linear convergence of the multi-marginal Sinkhorn algorithm

Abstract

The aim of this short note is to give an elementary proof of linear convergence of the Sinkhorn algorithm for the entropic regularization of multi-marginal optimal transport. The proof simply relies on: i) the fact that Sinkhorn iterates are bounded, ii) strong convexity of the exponential on bounded intervals and iii) the convergence analysis of the coordinate descent (Gauss-Seidel) method of Beck and Tetruashvili [1].
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Dates and versions

hal-03176512 , version 1 (22-03-2021)

Identifiers

  • HAL Id : hal-03176512 , version 1

Cite

Guillaume Carlier. On the linear convergence of the multi-marginal Sinkhorn algorithm. SIAM Journal on Optimization, 2022, 32 (2), pp.786-794. ⟨hal-03176512⟩
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