A comparison of reduced and unreduced symmetric KKT systems arising from Interior Point methods

We address the iterative solution of KKT systems arising in the solution of convex quadratic programming problems. Two strictly related and well established formulations for such systems are studied with particular emphasis on the effect of preconditioning strategies on their relation. Constraint and augmented preconditioners are considered, and the choice of the augmentation matrix is discussed. A theoretical and experimental analysis is conducted to assess which of the two formulations should be preferred for solving large-scale problems.