Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization (Q1681794)

The authors present a practical method for the interior point solution of a number of partial differential equations (PDE) -- constrained optimization problems with state and control constraints, by reformulating the minimization of the discretized system as a quadratic programming problem. In these approaches one is required to solve matrix systems of huge scale resulting from Newton iteration. A general methodology to design efficient preconditioners for such systems is proposed. This approach is derived from the matching strategy originally developed for a particular Poisson control problem [\textit{J. W. Pearson} and \textit{A. J. Wathen}, Numer. Linear Algebra Appl. 19, No. 5, 816--829 (2012; Zbl 1274.65187)]. Computational results show that this approach works well in practice.