2022
DOI: 10.48550/arxiv.2203.01633
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Numerical method for feasible and approximately optimal solutions of multi-marginal optimal transport beyond discrete measures

Abstract: We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general measures that are not necessarily discrete. By developing a relaxation scheme in which marginal constraints are replaced by finitely many linear constraints and by proving a specifically tailored duality result for this setting, we approximate the MMOT problem by a linear semiinfinite optimization problem. Moreover, we are able to recover a feasible and approximately optimal solution of th… Show more

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“…We refer also to[68] for a multidimensional version of[17], as well as[60] for a non-asymptotic version of[17],[68].…”
mentioning
confidence: 99%
“…We refer also to[68] for a multidimensional version of[17], as well as[60] for a non-asymptotic version of[17],[68].…”
mentioning
confidence: 99%