The Optimal Partial Transport Problem

By Alessio Figalli. 2010

229 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d427728531a7b24e584b000e72f012f1f2cf6801

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Multi-marginal optimal transport: theory and applications (2014, background): “In the former variant, uniqueness of solutions for infimal convolution type costs has been established with Kitagawa [48], under a natural and necessary condition on the marginals, extending work in the two marginal case of Caffarelli–McCann [11] and Figalli [30].”
BV Estimates in Optimal Transportation and Applications (2015, background): “The projection problem on Kf is a particular case of the so called partial transport problem, see [12, 13].”
Unbalanced optimal transport: Dynamic and Kantorovich formulations (2015, background): “The minimization problem over subcouplings introduced in Theorem 5.2 is a formulation of the optimal partial transport problem, a variant of optimal transport studied in [6, 9].”
Optimal transport from Lebesgue to Poisson (2010, background): “[Fig10] A. Figalli.”
Screening cell–cell communication in spatial transcriptomics via collective optimal transport (2023, background): “36).”
Hölder Continuity and Injectivity of Optimal Maps (2011, background): “This question is not merely of technical interest, since discontinuities in f± arise unavoidably in applications such as partial transport problems [10] [3] [15] [16].”
Scaling Algorithms for Unbalanced Transport Problems (2016, methodology): “If F 3 is the indicator of equality with a positive real number, this algorithm solves the partial optimal transport problem [19, 33] but more general F 3 can be considered such as, for instance, a range constraint on the total mass.”
The Monge–Ampère equation and its link to optimal transportation (2013, background): “In contrast with this, in [49] the author showed that C loc regularity is optimal: one can find two C ∞ densities on R, supported on two bounded intervals and bounded away from zero on their supports, such that the transport map is not C.”
Iterative Bregman Projections for Regularized Transportation Problems (2014, unknown): “The continuous partial optimal transport problem has been studied in Caf-farelli-McCann [18] and Figalli [32].”