  In this paper, we consider the generalised (higher order) Langevin equation
for the purpose of simulated annealing and optimisation of nonconvex functions.
Our approach modifies the underdamped Langevin equation by replacing the
Brownian noise with an appropriate Ornstein-Uhlenbeck process to account for
memory in the system. Under reasonable conditions on the loss function and the
annealing schedule, we establish convergence of the continuous time dynamics to
a global minimum. In addition, we investigate the performance numerically and
show better performance and higher exploration of the state space compared to
the underdamped and overdamped Langevin dynamics with the same annealing
schedule.
