Optimal control problems in density space

7a507f364fce7547f94b9a5b4a072c87?s=47 Wuchen Li
May 26, 2018
150

Optimal control problems in density space

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.

7a507f364fce7547f94b9a5b4a072c87?s=128

Wuchen Li

May 26, 2018
Tweet