The GRG Method

In the standard Solver, NLP problems are solved with the GRG (Generalized Reduced Gradient) method as implemented in Lasdon and Waren's GRG2 code. This method and specific implementation have been proven in use over many years as one of the most robust and reliable approaches to solving difficult NLP problems.

The GRG method is subject to the intrinsic limitations cited above on its ability to find the globally optimal solution. However, limited guarantees can be made about the GRG method's ability to find a "local optimum," in particular where the objective function and all of the constraints are twice continuously differentiable. When these are combined with your knowledge of problem structure in a specific case, the result will often be a definitive "optimal solution." For more information on this topic, please consult the references cited in the Using Frontline's Solvers.

As with the Simplex method, the GRG method in the standard Solver uses a "dense" problem representation, and its memory and solution time increases with the number of variables times the number of constraints. It is also subject to problems of numerical instability, which may be even more severe than for LP and QP problems. In the future, Frontline Systems plans to release a Large-Scale NLP Solver based on Lasdon and Waren's LSGRG code, which uses sparse storage methods and more sophisticated numerical techniques specific to nonlinear models.