Andreas Prohl, Professor of Mathematics, Tübingen University Title: Numerical Methods to solve the Linear-Quadratic Optimal Control problem with SPDEs

Abstract:

I propose different implementable algorithms to approximate the minimizer of an optimal control problem, which consists of a quadratic functional subject to

a linear stochastic PDE. One construction is based on the 'open loop' approach, where to simulate backward SPDEs is the bottleneck in terms of efficiency.

The second construction is based on the 'closed loop' approach, which involves the Riccati-equation as key ingredient.

I discuss the tools that are needed in related numerical analyses to verify optimal rates of convergence for both approaches.

This is joint work with Y. Wang (Southwest U, China).