Existence of potentials for non-traditional cost functions

Abstract: In this talk, we will present a new approach to the problem of existence of a potential for the optimal transport problem and apply it to non-traditional cost functions (i.e. costs that may attain infinite values). As a by-product, we give a new transparent proof of Rockafellar-Ruschendorf theorem. As an example of a non-traditional cost, we discuss the polar cost, which is particularly interesting as it induces the polarity transform and the class of geometric convex functions. This is joint work with S. Artstein-Avidan and S. Sadovsky.

analysis of PDEsmetric geometryprobability

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

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