Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula
arXiv:1805.01636
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.
References in corpus (4)
- Perspectives on characteristics based curse-of-dimensionality-free numerical approaches for solving Hamilton-Jacobi equations
- A discrete Schrodinger equation via optimal transport on graphs
- Geodesic of minimal length in the set of probability measures on graphs
- Algorithm for Overcoming the Curse of Dimensionality for State-dependent Hamilton-Jacobi equations