A Globally Convergent LCL Method for Nonlinear Optimization
Michael P. Friedlander, Michael A Saunders
Abstract
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 \ 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 only as heuristics. The new algorithm has been implemented in , with the option to use either the or Fortran codes to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a nonlinear subset of the , , and HS test-problem sets, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.
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