Numerical Methods for Mean-Field-Type Optimal Control Problems

Understand

In this article, two methods for solving mean-field type optimal control problems are proposed and investigated.

• The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal condition obtained by linearizing the cost function.
• The terminal condition is updated by solving a Fokker-Planck equation.
• The first method can be seen as a gradient method and uses in an essential manner the convexity of the set of probability distributions.