A Primal-Dual Regularized Interior-Point Method for Convex Quadratic Programs
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Thu, 29/04/2010 14:00 |
Prof Dominique Orban (Ecole Polytechnique de Montréal and GERAD) |
Computational Mathematics and Applications  |
Rutherford Appleton Laboratory, nr Didcot |
| 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. This is joint work with Michael Friedlander, University of British Columbia, Canada | |||