A Globally Convergent Linearly Constrained Lagrangian Method for Nonlinear Optimization

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 from 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.