Block Diagonal Parareal Preconditioner for Parabolic Optimal Control Problems
Tarek Mathew | Sarkis, Marcus | Schaerer, Christian
Optimal control | Block diagonal preconditioner | Parareal
We describe a block matrix iterative algorithm for solving a linear-quadratic parabolic optimal control problem (OCP) on a finite time interval. We derive a reduced symmetric indefinite linear system involving the control variables and auxiliary variables, and solve it using a preconditioned MINRES iteration, with a symmetric positive definite block diagonal preconditioner based on the parareal algorithm. Theoretical and numerical results show that the preconditioned algorithm converges at a rate independent of the mesh size $h$, and has parallel scalability.