Optimization Modeling with Spreadsheets, 3rd Edition

8 NONLINEAR PROGRAMMING

In Chapter 1, we introduced the optimization capability of Solver with a simple revenue-maximization problem that illustrated the Generalized Reduced Gradient (GRG) Nonlinear procedure, which is Excel’s nonlinear solver. Then, in Chapters 2–7, we focused on linear programming models, solving them with Excel’s linear solver. In this chapter, we return to the nonlinear solver and examine the types of optimization problems it can handle.

Taken literally, the term nonlinear programming refers to the formulation and solution of constrained optimization problems that are anything but linear. However, that isn’t a wholly accurate assessment of the GRG algorithm’s capability. Two features are important in this regard. First, mathematically speaking, linear programming models are actually a subset of nonlinear programming models. That is, the GRG algorithm can be used to solve linear as well as nonlinear programs. However, for linear programming, we use the linear solver because it is numerically more dependable than the GRG algorithm and provides a more extensive sensitivity analysis. The GRG algorithm provides an abbreviated sensitivity analysis, and it may also have difficulty locating a feasible solution when one exists. Still, there is nothing wrong, in principle, with using the GRG algorithm to solve a linear problem.

The second feature to keep in mind is that the GRG algorithm has limitations as a nonlinear solver. In particular, it is mainly suited ...