On the computation of the infinity Wasserstein distance and the Wasserstein Projection Problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909736898658304 |
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| author | Auricchio, Gennaro Loli, Gabriele Veneroni, Marco |
| author_facet | Auricchio, Gennaro Loli, Gabriele Veneroni, Marco |
| contents | 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 $p\in[1,\infty]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the computation of the infinity Wasserstein distance and the Wasserstein Projection Problem Auricchio, Gennaro Loli, Gabriele Veneroni, Marco Optimization and Control 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 $p\in[1,\infty]$. |
| title | On the computation of the infinity Wasserstein distance and the Wasserstein Projection Problem |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.10589 |