Augmentation Preconditioning for Saddle Point Systems Arising from Interior Point Methods

We investigate a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1, 1) block of the saddle point matrix. We demonstrate performance of the preconditioner on problems from the NETLIB and CUTEr test suites. The numerical experiments include results based on inexact inner iterations, and comparisons of the proposed techniques with constraint preconditioners. Approximations to the preconditioner are considered for systems with simple (1, 1) blocks. The preconditioning approach is also extended to deal with stabilized systems. We show that for stabilized saddle point systems a minimum residual Krylov method will converge in just two iterations.