### Dominique Orban (Ecole Polytechnique de Montréal, Canada)

#### A primal-dual regularized interior-point method for convex quadratic programs

*Joint work with Michael Friedlander (University of British Columbia, Canada).*

*Wednesday 5 May 2010 at 15.30, JCMB 6206 - Joint with NAIS*

##### Abstract

Interior-point methods for linear and convex quadratic programming require the
solution of a sequence of symmetric indefinite linear systems which are used
to derive search directions. Safeguards are typically required in order to
handle free variables or rank-deficient Jacobians. We propose a consistent
framework and accompanying theoretical justification for regularizing these
linear systems. Our approach is akin to the proximal method of multipliers
and can be interpreted as a simultaneous proximal-point regularization of the
primal and dual problems. The regularization is termed "exact" to emphasize
that, although the problems are regularized, the algorithm recovers a solution
of the original problem. Numerical results will be presented. If time permits
we will illustrate current research on a matrix-free implementation.

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