A null-space method for computing the search direction in the general inertia-controlling method for dense quadratic programming

The inertia-controlling strategy in active set methods consists of choosing the working set so that the reduced Hessian never has more than one non-positive eigenvalue. Usually, this strategy has been implemented by permitting to delete constraints only at stationary points. In a general inertia-controlling method constraints may be deleted at non-stationary points. A null-space method for dense quadratic programming is presented, in which only one triangular system has to be solved at each iteration for computing the search direction. This method takes advantage of previously developed recurrence formulas for updating the search direction when the working set changes.