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Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
Alberto Gonz\'alez-Sanz, Marcel Nutz, Andr\'es Riveros Valdevenito
https://arxiv.org/abs/2509.08547

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. Here quadratic regularization means that transport couplings are penalized by the squared $L^2$ norm, or equivalently the $χ^2$ divergence. While a number of computational approaches have been shown to work in practice, quadratic regularization is analytically less tractable than entropic, and we are not aware of a previous theoretica…