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Constrained dynamical optimal transport and its Lagrangian formulation

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arxiv 1807.00937 v2 pith:FZ233ULN submitted 2018-07-03 math.OC

Wuchen Li , Stanley Osher This is my paper · ORCID
classification math.OC
keywords constraineddynamicalformulationoptimalparameterizedprobabilityproblemstransport
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We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In this case, we derive a simple formulation for the constrained dynamical OT.

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  1. Convex Relaxations for the Optimization of Markov Processes

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    Sequential-coupling convex relaxations using local marginals and cluster moments solve high-dimensional Markov process optimization, recovering Benamou–Brenier dynamics and general kernels as special cases.

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