8 papers · 1 filter
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…
Entropic regularization of Monge's problem
Marcel Nutz, Chenyang Zhong
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost in dimension . We develop a co…
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 regulari…
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…