A Preconditioner For Linear Systems Arising From Interior-Point Optimization 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 analyze its spectral characteristics, utilizing projections onto the null space of the constraint matrix, and 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.