  For optimization problems with nonlinear constraints, linearly constrained
Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to
linearized constraints. These methods converge rapidly near a solution but may
not be reliable from arbitrary starting points. The well known example \MINOS\
has proven effective on many large problems. Its success motivates us to
propose a globally convergent variant. Our stabilized LCL method possesses two
important properties: the subproblems are always feasible, and they may be
solved inexactly. These features are present in \MINOS only as heuristics.
  The new algorithm has been implemented in \Matlab, with the option to use
either the \MINOS or \SNOPT Fortran codes to solve the linearly constrained
subproblems. Only first derivatives are required. We present numerical results
on a nonlinear subset of the \COPS, \CUTE, and HS test-problem sets, which
include many large examples. The results demonstrate the robustness and
efficiency of the stabilized LCL procedure.
