Abstract
We present new algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to derive a coupled forward-backward optimality system, which can then be solved using a time domain decomposition. In case of a spatial decomposition, there is only one standard way to apply these algorithms. However, due to the forward-backward structure of the optimality system, different variants can be found for these algorithms. We show their convergence behavior and the optimal relaxation parameter. Our analysis reveals that the most natural algorithms sometimes are only good smoothers, and there are better choices which lead to efficient solvers.
卢 柳 䃅
Postdoctoral Fellow in Applied Mathematics
My research interests include Numerical Analysis, Mathematical Biology, Scientific Computing, Optimization and Control.