Heuristics for implementation of a hybrid preconditioner for interior-point methods

This article presents improvements to the hybrid preconditioner previously developed for the solution through the conjugate gradient method of the linear systems which arise from interior-point methods. The hybrid preconditioner consists of combining two preconditioners: controlled Cholesky factorization and the splitting preconditioner used in different phases of the optimization process. The first, with controlled fill-in, is more efficient at the initial iterations of the interior-point methods and it may be inefficient near a solution of the linear problem when the system is highly ill-conditioned; the second is specialized for such situation and has the opposite behavior. This approach works better than direct methods for some classes of large-scale problems. This work has proposed new heuristics for the integration of both preconditioners, identifying a new change of phases with computational results superior to the ones previously published. Moreover, the performance of the splitting preconditioner has been improved through new orderings of the constraint matrix columns allowing savings in the preconditioned conjugate gradient method iterations number. Experiments are performed with a set of large-scale problems and both approaches are compared with respect to the number of iterations and running time.57959