Relative entropy weighted optimization is convex optimization problem over the space of probability measures. Many convex optimization problems can be rephrased as such a problem. This is particularly useful since this problem type admits a quasi-explicit solution (i.e. as the expectation over a random variable), which immediately provides a Monte-Carlo method for numerically computing the solution of the optimization problem.
In this talk we discuss the background and application of this approach to stochastic optimal control problems, which may be considered as relative entropy weighted problems with Wiener space as probability space, and its connection with the theory of large deviations for Brownian functionals. As a particular application we discuss the minimization of the local time in a given point of Brownian motion with drift.