output
20142022
most citedStochastic Optimization for Large-scale Optimal Transport

147 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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8 papers · 1 filter

math.OC2021★ 3 cited

Regularity theory and geometry of unbalanced optimal transport

Thomas Gallouët, Roberta Ghezzi, François-Xavier Vialard

Using the dual formulation only, we show that the regularity of unbalanced optimal transport also called entropy-transport inherits from the regularity of standard optimal transpor…

math.OC2018★ 1 cited

On Representer Theorems and Convex Regularization

Claire Boyer, Antonin Chambolle, Yohann De Castro +3

We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms.…

math.OC2017★ 14 cited

A Low-Rank Approach to Off-The-Grid Sparse Deconvolution

Paul Catala, Vincent Duval, Gabriel Peyré

We propose a new solver for the sparse spikes deconvolution problem over the space of Radon measures. A common approach to off-the-grid deconvolution considers semidefinite (SDP) r…

math.OC2017

A study of the dual problem of the one-dimensional L-infinity optimal transport problem with applications

Luigi De Pascale, Jean Louet

The Monge-Kantorovich problem for the infinite Wasserstein distance presents several peculiarities. Among them the lack of convexity and then of a direct duality. We study in dimen…

math.OC2017★ 5 cited

The entropic regularization of the Monge problem on the real line

Simone Di Marino, Jean Louet

We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance c(x, y) = |y -- x|. The selected plan at the limit is, a…

math.OC2016★ 147 cited

Stochastic Optimization for Large-scale Optimal Transport

Genevay Aude, Marco Cuturi, Gabriel Peyré +1

Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited becau…

math.OC2016★ 90 cited

Geometric properties of solutions to the total variation denoising problem

Antonin Chambolle, Vincent Duval, Gabriel Peyré +1

This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-…

math.OC2015★ 81 cited

A Sparse Multi-Scale Algorithm for Dense Optimal Transport

Bernhard Schmitzer

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to contin…