Robust Iterative Solution of a Class of Time‐Dependent Optimal Control Problems
John W. Pearson, Martin Stoll, Andy Wathen · PAMM · 2012
Abstract The fast iterative solution of optimal control problems, and in particular PDE‐constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time‐dependent PDE‐constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approximate the (1, 1)‐block and Schur complement of the saddle point system that results from solving this problem, and therefore derive a block diagonal preconditioner to be used within the MINRES algorithm. We present numerical results to demonstrate that this approach yields a robust solver with respect to step‐size and regularization parameter. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)