### Yiming Yan (University of Edinburgh)

#### Optimal active-set prediction for interior point methods using controlled perturbations

*Wednesday 27 November 2013 at 15.30, JCMB 6301*

##### Abstract

We propose the use of controlled perturbations to address the well-known and
challenging question of optimal active-set prediction for interior point
methods. Namely, in the context of a standard-form linear programming problem,
we consider perturbing the inequality constraints/bounds so as to enlarge the
feasible set. We show that if the perturbations are chosen appropriately, the
solution of the original problem lies on or close to the central path of the
perturbed problem and that a primal-dual path-following algorithm applied to
the perturbed problem is able to predict the optimal active-set of the original
problem when the duality gap (for the perturbed problem) is not too small.
Encouraging preliminary numerical experience is reported when comparing the
activity prediction for the perturbed and unperturbed formulations for the
purpose of crossover to simplex.

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