Active-set prediction in quadratic programming using interior point methods and controlled perturbations

Abstract

In this paper, we extend the idea of using controlled perturbations to enhance the capabilities of active-set prediction for interior point methods for convex Quadratic Programming (QP) problems. Namely, we consider perturbing the inequality constraints (by a small amount) so as to enlarge the feasible set. We show that if the perturbations are chosen judiciously, then there exists a primal-dual pair of points which is close to the optimal solution of the perturbed problems and the corresponding active and inactive sets at this point are the same as the optimal active and inactive sets at an optimal solution of the original QP problems. Additionally, we prove that the optimal tripartition of the original problems can also be predicted by solving the perturbed ones. Furthermore, encouraging preliminary numerical experience is also presented for the QP case.