A primal-dual active set algorithm is developed for Nonlinear optimization with polyhedral constraints. The algorithm consists of a nonmonotone gradient projection phase implemented by dual active set techniques, an unconstrained optimization phase in the subspace determined by the active set, and a set of rules for branching between the two phases. Global convergence to a stationary point is established. For a nondegenerate stationary point, the algorithm eventually reduces to an unconstrained optimization in a subspace without restarts. Similarly, for a degenerate stationary point where the strong second-order sufficient optimality condition holds, the algorithm eventually reduces to unconstrained optimization in a subspace. A specific implementation of the algorithm is given which exploits a new dual active set algorithm for the gradient projection step and the limited memory CG\_DESCENT algorithm for unconstrained optimization. Numerical results are presented.