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{\large Tyrone Rees \\
{\bf A block diagonal preconditioner for PDE constrained optimization}}

Oxford University Computing Laboratory \\ Wolfson Building \\ Parks Road \\ Oxford \\ OX1 3QD \\ UK
\\
{\tt tyrone.rees@comlab.ox.ac.uk}\\
Andy Wathen\\
Sue Dollar\end{center}

Optimization problems where the constraint is a partial differential
equation are important in many areas of the sciences and engineering. One
such formulation is the Dirichlet distributed control problem, which can
be written as a saddle point system. Here we present an ‘all-at-once’
method based on preconditioned MINRES, together with an efficient,
optimal preconditioner which uses multigrid methods, to solve such
problems.


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