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We propose the use of controlled perturbations to address the challengingquestion of optimal active-set prediction for interior point methods. Namely,in the context of linear programming, we consider perturbing the inequalityconstraints/bounds so as to enlarge the feasible set. We show that if theperturbations are chosen appropriately, the solution of the original problemlies on or close to the central path of the perturbed problem. We also findthat a primal-dual path-following algorithm applied to the perturbed problem isable to accurately predict the optimal active set of the original problem whenthe duality gap for the perturbed problem is not too small; furthermore,depending on problem conditioning, this prediction can happen sooner thanpredicting the active set for the perturbed problem or when the original one issolved. Encouraging preliminary numerical experience is reported when comparingactivity prediction for the perturbed and unperturbed problem formulations.

Active-set prediction for interior point methods using controlled perturbations