Quadratic Functions

The last two examples above, +C1^2 or +C1*C2, are simple instances of quadratic functions of the variables. A more complex example would be:

+2*C1^2+3*C2^2+4*C1*C2+5*C1

A quadratic function is a sum of terms, where each term is a (positive or negative) constant (again called a coefficient) multiplied by a single variable or the product of two variables. Common uses for quadratic functions are to compute the mean squared error in a curve-fitting application, or the variance or standard deviation of security returns in a portfolio optimization application.

What if you have already created a complex spreadsheet model without using functions like @SUMPRODUCT, and you aren't sure whether your objective function and constraints are linear or nonlinear functions of the variables? A quick way to find out is to try solving the model with Assume Linear Model box checked in the Solver Options dialog. Although this test is not 100% foolproof, it will in most cases return an error message if the problem contains nonlinear functions of the variables. In any case, the next step is to look closely at the formulas in your spreadsheet and to try rewriting them using the @SUMPRODUCT product. Your effort will be rewarded in most cases by a better understanding of your model, as well as a problem which Frontline's enhanced Solvers can handle efficiently.