Preconditioning methods for linear systems arising in constrained optimization problems

Preconditioning methods for matrices on saddle point form, as typically arising in equality constrained optimization problems, are surveyed. Special consideration is given to two methods: a nearly symmetric block incomplete factorization preconditioning method and a preconditioner on the same saddle point form as the given matrix. Both methods result in eigenvalues with positive real parts and small or zero imaginary parts. The behaviour of the methods are illustrated by solving a regularized Stokes problem. Copyright (C) 2002 John Wiley Sons, Ltd.