SCAIM Seminar: Dominique Orban (École Polytechnique Montréal)

Interior-point methods for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear systems to derive search directions. Safeguards are typically required to handle free variables or rank-deficient constraints. 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. This is joint work with Michael Friedlander, University of British Columbia, Canada.