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@inproceedings{Carlen2002ConstrainedSD, title={Constrained steepest descent in the 2-Wasserstein metric}, author={Eric A. Carlen and Wilfrid Gangbo}, year={2002} }

- Published 2002

We study several constrained variational problems in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density F0 on Rd and a time-step h > 0, we seek to minimize I(F ) = hS(F )+W 2 2 (F0, F ) over all of the probability densities F that have the same mean and variance as F0, where S(F ) is the entropy of F . We prove existence of minimizers. We also analyze the induced geometry of the set of densitiesâ€¦Â CONTINUE READING

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