On the identification of local minimizers in inertia-controlling
methods for quadratic programming
The verification of a local minimizer of a general (i.e., nonconvex)
quadratic program is in general an NP-hard problem. The difficulty
concerns the optimality of certain points (which we call dead
points) at which the first-order necessary conditions for
optimality are satisfied, but strict complementarity does not hold.
Inertia-controlling quadratic programming (ICQP) methods form an
important class of methods for solving general quadratic programs. We
derive a computational scheme for proceeding at a dead point that is
appropriate for a general ICQP method.