Abstract
An optimal control problem in the space of probability measures and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a smooth Fourier-Wasserstein metric. A comparison result between the Lipschitz viscosity sub- and supersolutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity solution.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 903-923 |
| Number of pages | 21 |
| Journal | SIAM Journal on Control and Optimization |
| Volume | 62 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2024 |
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics
Keywords
- McKean-Vlasov
- Wasserstein metric
- mean-field games
- viscosity solutions