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{\large Martin Stoll \\
{\bf A Bramble-Pasciak-like method with applications in optimization.}}

Oxford University Computing Laboratory \\ 
Oxford, England \\
{\tt martin.stoll@comlab.ox.ac.uk} \\
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The Bramble-Pasciak Conjugate Gradient algorithm is a widely used tool in the finite element community. Motivated by a reformulation of the linear system in saddle point form, we introduce Bramble-Pasciak-like methods that can be used to solve problems coming from optimization. We illustrate that the eigenvalues for the preconditioned matrix in this setup have a very similar (sometimes equivalent) structure to the preconditioned matrix of a method which uses a constraint preconditioner. We furthermore give numerical results for optimization examples.

The author would like to thank Sue Dollar, Nick Gould and Andy Wathen for their helpful comments.
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