In this presentation, we study an optimal control problem for the stochastic Landau- Lipschitz-Gilbert equation on a bounded domain inRd (d = 1,2,3). We first establish existence of a relaxed optimal control for relaxed version of the problem. As the control acts linearly in the equation, we then establish existence of an optimal control for the underlying problem. Moreover, convergence of a structure preserving finite element approximation for d = 1 and physically relevant computational studies will be discussed.

Furthermore, we study an optimal control problem of N interacting ferromagnetic particles which are immersed into a heat bath through the application of a distributed exterior field minimizing a quadratic cost functional. With the dynamic programming principle, we show the existence of a unique strong solution of the optimal control problem. With a Hopf-Cole transformation the related nonlinear Hamilton-Jacobi-Bellman equation is re-cast into a linear PDE on the manifold M = (S2)N , whose classical solution is represented with a Feynman-Kac formula. We propose to use this probabilistic representation to numerically study optimal switching dynamics with Monte- Carlo simulations