For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form "minimize an augmented Lagrangian function subject to linearized constraints". Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. The well known software package MINOS has proven effective on many large problems. Its success motivates us to propose a variant of the LCL method that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. 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, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.
Preprint ANL/MCS-P1015-1202, December 2002 (Revised March 2004); Mathematics and Computer Science Division; Argonne National Laboratory