An inexact Shooting Method using Proper Orthogonal Decomposition for Parabolic Optimal Control Problems

This paper is devoted to a numerical solution technique for linear quadratic parabolic optimal control problems using the model order reduction technique of Proper Orthogonal Decomposition (POD). The proposed technique is a direct shooting method where in each iteration, instead of solving the PDE with an expensive FE method, this computation will be substituted by the POD-Galerkin method. This method is many faster than shooting method and a comparison to FE method show that it has good accuracy.