For any indefinite matrix K, it is shown that the UTDU factorization can be modified at nominal cost to provide an "exact" preconditioner for SYMMLQ. Code is given for overwriting the blockdiagonal matrix D produced by MA27. The KKT systems arising in barrier methods for linear and nonlinear programming are studied, and preconditioners for use with SYMMLQ are derived. For nonlinear programs a preconditioner is derived from the "smaller" KKT system associated with variables that are not near a bound. For linear programs several preconditioners are proposed, based on a square nonsingular matrix B that is analogous to the basis matrix in the simplex method. The aim is to facilitate solution of full KKT systems rather than equations of the form AD2ATAr r when the latter become excessively ill conditioned.
Iterative solution of the full KKT system is explored in REF .
PRECONDITIONERS FOR INDEFINITE SYSTEMS ARISING IN OPTIMIZATION
SIAM J. Matrix Analysis Applications
SIAM J. Matrix Analysis Applications
Computer Science Mathematics