\documentclass{report}
\usepackage{amsmath,amssymb}
\setlength{\parindent}{0mm}
\setlength{\parskip}{1em}
\begin{document}
\begin{center}
\rule{6in}{1pt} \
{\large Tyrone Rees \\
{\bf Preconditioning Iterative Methods for the Optimal Control of the Stokes Equations}}

Mathematical Institute \\ 24-29 St Giles' \\ Oxford \\ OX1 3LB \\ UK
\\
{\tt tyrone.rees@maths.ox.ac.uk}\end{center}

Solving problems regarding the optimal control of partial differential
equations (PDEs) -- also known as PDE-constrained optimization -- is a
frontier area of numerical analysis. Of particular interest is the
problem of flow control, where one would like to effect some desired flow
by exerting, for example, an external force. The bottleneck in many
current algorithms is the solution of the optimality system -- a system
of equations in saddle point form that is usually very large and
ill-conditioned. In this talk I will describe a block-diagonal
preconditioner for the minimal residual method which can be applied to
such problems where the PDEs are the Stokes equations. We will consider
only distributed control here, although other problems -- for example
boundary control -- can be solved in a similar way. I will present
numerical results, and compare these with those obtained by solving the
equivalent forward problem using similar techniques.


\end{document}
