Stabilized Optimization Via an NCL Algorithm

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 the state-of-the-art solvers that we tested, because of singularity in the Jacobian of the active constraints. Algorithm NCL with IPOPT as subproblem solver proves to be effective, with IPOPT using second derivatives and successfully warm starting each subproblem.