Applied Math And Analysis Seminar
Monday, August 20, 2018, 9:30am, Physics 047
Li Wang (University of Minnesota)
Primal dual methods for Wasserstein gradient flows
Abstract:- In this talk, I will introduce a variational method for nonlinear
equations with a gradient flow structure, which arise widely in
applications such as porous median flows, material science, animal
swarms, and chemotaxis. Our method builds on the JKO framework and a
reformulation of the Wasserstein distance into a convex optimization
with a linear PDE constraint. As a result, we end up with one nested
structure of optimization problem with two time scales, and we adopt a
recent primal dual three operator splitting scheme. Thanks to the
variational structure, our method has a built-in positivity
preserving, entropy decreasing properties, and overcomes stability
issue due to the strong nonlinearity and degeneracy. Upon
discretization of the PDE constraint, we also show the Γ−convergence
of the fully discrete optimization towards the semi-discrete JKO
scheme. This is a joint work with Jose Carrillo, Katy Craig, and
Chaozhen Wei.
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