An algorithm for indefinite quadratic programming based on a partial Cholesky factorization

A new algorithm is described for quadratic programming that is based on a partial Cholesky factorization that uses a diagonal pivoting strategy and allows computation of null of negative curvature directions. The algorithm is numerically stable and has shown efficiency solving positive-definite and indefinite problems. It is specially interesting in indefinite cases because the initial point does not need to be a vertex of the feasible set. The authors thus avoid introducing artifical constraints in the problem, which turns out to be very efficient in parametric programming. At the same time, techniques for updating matrix factorizations are used.