{"ID":2882315,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.10589","arxiv_id":"2508.10589","title":"On the computation of the infinity Wasserstein distance and the Wasserstein Projection Problem","abstract":"Computing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various applied fields. However, the practical applicability of these objects is limited by two factors: either the associated quantities are computationally prohibitive or there is a lack of available algorithms capable of calculating them. In this paper, we propose a novel class of Linear Programming problems and a routine that allows us to compute the infinity Wasserstein distance and to compute a projection of a probability measure over a generic subset of probability measures with respect to any $p$-Wasserstein distance with $p\\in[1,\\infty]$.","short_abstract":"Computing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various applied fields. However, the practical applicability of these objects is limited by two factors: either the associated quantities are computat...","url_abs":"https://arxiv.org/abs/2508.10589","url_pdf":"https://arxiv.org/pdf/2508.10589v1","authors":"[\"Gennaro Auricchio\",\"Gabriele Loli\",\"Marco Veneroni\"]","published":"2025-08-14T12:28:27Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}