<ul><li>Researchers have developed a computational approach that uses Sum-of-Squares (SOS) programming to verify the non-negativity of the Ma-Trudinger-Wang (MTW) tensor associated with ground cost functions in optimal transport.</li><li>The MTW tensor provides a measure of curvature in optimal transport and is crucial for establishing continuity in the Monge optimal transport map.</li><li>The proposed approach not only provides certificates of non-negativity for the MTW tensor but also computes an inner approximation of the region where MTW non-negativity holds.</li><li>The SOS programming method has been applied to various practical ground cost functions to approximate the regions of regularity in their corresponding optimal transport maps.</li></ul>

Sum-of-Squares Programming for Ma-Trudinger-Wang Regularity of Optimal Transport Maps

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