Marcel Nutz

collaborators

14 papers

math.AP2026

Sharp Asymptotics for Regularized Optimal Transport

Carlos Cardoso-PerellÃ³, Alberto GonzÃ¡lez-Sanz, Marcel Nutz

We study the small-regularization limit for $L^{p}$ -regularized optimal transport with $1 < p < \infty$ and for entropically regularized optimal transport (EOT). The exact first-order (r…

math.ST2026

Finite-sample bounds for regularized optimal transport

Alberto GonzÃ¡lez-Sanz, Marcel Nutz, Austin J. Stromme

We study the sample complexity of regularized optimal transport for general convex regularizations including the Kullback--Leibler divergence and $L^{p}$ penalties. Our main results…

math.OC2026

Stability of Quadratically Regularized Optimal Transport

Alberto GonzÃ¡lez-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…

math.OC2026

Polyak-Lojasiewicz Inequality for Quadratically Regularized Optimal Transport

Alberto GonzÃ¡lez-Sanz, Marcel Nutz, AndrÃ©s 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…

math.OC2026

Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport

In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regulari…

math.OC2026

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 $c (x, y) = ∥ x - y ∥$ in dimension $d > 1$ . We develop a co…