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.
Current 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996