Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula
Numerical Analysis
2018-05-07 v1 Analysis of PDEs
Optimization and Control
Abstract
We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dimensionality nature of HJD by proposing a generalized Hopf formula in density space. The formula transfers optimal control problems in density space, which are constrained minimizations supported on both spatial and time variables, to optimization problems over only spatial variables. This transformation allows us to compute HJD efficiently via multi-level approaches and coordinate descent methods.
Cite
@article{arxiv.1805.01636,
title = {Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula},
author = {Yat Tin Chow and Wuchen Li and Stanley Osher and Wotao Yin},
journal= {arXiv preprint arXiv:1805.01636},
year = {2018}
}