Optimal Control and Numerical Methods for Hamilton-Jacobi-Bellman Equations

This seminar will explore the mathematical framework of optimal control, emphasising the challenges arising from the nonlinear structure of the problem, including issues related to the uniqueness of solutions and the role of viscosity solutions. In the first half, we will provide an overview of these challenges, highlighting the relevance of optimal control in various applications. The second half will focus on numerical methods for Hamilton-Jacobi-Bellman (HJB) equations, such as finite element methods and Monte Carlo techniques. A key case study on ferromagnetic materials will illustrate how these numerical methods can be applied in practice, addressing the specific complexities posed by the magnetic structure.