4 citations · 9 across the 30 of their papers we have counts for
9 papers · 1 filter
Geometry and Convergence of Quadratically Regularized Optimal Transport I
Alberto González-Sanz, Marcel Nutz
We establish sharp convergence rates for quadratically regularized optimal transport with quadratic cost in the regime of small regularization . In particular, we quan…
Stability of Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz
Quadratically regularized optimal transport (QOT) is a sparse alternative to entropic optimal transport. We develop a quantitative stability theory for QOT under perturbations of t…
Polyak-Lojasiewicz Inequality for Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential sc…
Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regulari…
Identifiability and Exact Reconstruction of the Optimal Transport Cost on Finite Spaces
Alberto González-Sanz, Michel Groppe, Axel Munk
The goal of optimal transport (OT) is to find optimal assignments or matchings between data sets which minimize the total cost for a given cost function. However, sometimes the cos…
Sparsity of Quadratically Regularized Optimal Transport: Scalar Case
Alberto González-Sanz, Marcel Nutz
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling has sparse support for small regulariz…
Monotonicity in Quadratically Regularized Linear Programs
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience sugges…
Quantitative Convergence of Quadratically Regularized Linear Programs
Alberto González-Sanz, Marcel Nutz
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penal…
Nonlinear Inverse Optimal Transport: Identifiability of the Transport Cost from its Marginals and Optimal Values
Alberto González-Sanz, Michel Groppe, Axel Munk
The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem,…