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- W4387623401 abstract "In this work, we propose a novel implementation of Newton's method for solving semi-discrete optimal transport (OT) problems for cost functions which are a positive combination of $p$-norms, $1<p<infty$. It is well understood that the solution of a semi-discrete OT problem is equivalent to finding a partition of a bounded region in Laguerre cells, and we prove that the Laguerre cells are star-shaped with respect to the target points. By exploiting the geometry of the Laguerre cells, we obtain an efficient and reliable implementation of Newton's method to find the sought network structure. We provide implementation details and extensive results in support of our technique in 2-d problems, as well as comparison with other approaches used in the literature." @default.
- W4387623401 created "2023-10-14" @default.
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- W4387623401 date "2023-10-11" @default.
- W4387623401 modified "2023-10-15" @default.
- W4387623401 title "Solving Semi-Discrete Optimal Transport Problems: star shapedeness and Newton's method" @default.
- W4387623401 doi "https://doi.org/10.48550/arxiv.2310.07489" @default.
- W4387623401 hasPublicationYear "2023" @default.
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