For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly-constrained (LCL) augmented-Lagrangian approaches of LANCELOT and MINOS to an algorithm that solves a sequence of nonlinearly constrained augmented Lagrangian subproblems whose nonlinear constraints satisfy the LICQ everywhere. The NCL algorithm is implemented in AMPL and tested on large instances of a tax policy model that could not be solved directly by any of the state-of-the-art solvers that we tested due to degeneracy. Algorithm NCL with IPOPT as subproblem solver proves to be effective, with IPOPT achieving warm starts on each subproblem.