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Speaker: Rene Cabrera, University of Texas, Austin
Title: An optimal transport problem with interaction effects
Abstract: I will talk about a modification of the Monge-Kantorovich problem taking into account interaction effects via path dependency between particles. We prove the existence of solutions under mild conditions on the data, and after imposing stronger conditions, we characterize the minimizers by relating them to an auxiliary Monge-Kantorovich problem of the more standard kind. With this notion of how particles interact and travel along paths, we produce a dual problem. The main novelty here is to incorporate an interaction effect to the optimal path transport problem. Lastly, our results include an extension of Brenier’s theorem on optimal transport maps and a formulation of the celebrated Benamou-Brenier theory with interaction effects.