  A Newton-type active set algorithm for large-scale minimization subject to
polyhedral constraints is proposed. The algorithm consists of a gradient
projection step, a second-order Newton-type step in the null space of the
constraint matrix, and a set of rules for branching between the two steps. We
show that the proposed method asymptotically takes the Newton step when the
active constraints are linearly independent and a strong second-order
sufficient optimality condition holds. We also show that the method has a
quadratic rate of convergence under standard conditions. Numerical experiments
are presented illustrating the performance of the algorithm on the CUTEst and
on a specific class of problems for which finding second-order stationary
points is critical.

Optimization and Control