Premium Solver Platform - Automatic Detection of Linearity and Convexity

Automatic Detection of Linearity and Convexity

The Premium Solver Platform's Polymorphic Spreadsheet Interpreter can analyze the formulas in your Excel model, to determine if they are linear, quadratic, smooth nonlinear, or non-smooth functions of the decision variables.  And the Platform can often determine whether your smooth nonlinear functions are convex -- the key property that makes it possible to solve your model quickly and reliably, to very large size. 

To analyze your model, you simply click the Model button in the main Solver Parameters dialog, to display the Solver Model dialog.  Click the Check Model button to determine your model's Gradients, Structure or Convexity.

This diagnosis of the EXAMPLE1 model shipped with the Premium Solver Platform shows that it is an LP Convex (linear programming) problem, with 3 variables that always occur linearly in the objective and constraints, and 6 linear functions. 

If we deliberately modify the calculation of Chassis parts used so this formula is no longer linear, and re-check the model, it is diagnosed as NLP NonCvx (nonlinear and non-convex), with 5 out of 6 functions linear, and 1 out of 3 variables occurring linearly (since the Speakers variable doesn't occur in the calculation of Chassis parts used).

In a large model with hundreds or thousands of variables and constraints, finding a single nonlinear or nonsmooth formula is like finding a needle in a haystack -- but the Premium Solver Platform will find it for you!  On the Options tab, select Linear for Desired Model, and check the box to Show Exceptions to Desired Model, then click the Check Model button again. 

This inserts a Structure Report into your workbook (click the report to see it full size):

Model Structure Report (45759 bytes)

This report shows one formula that is an exception to a linear model, at cell C11 on worksheet EXAMPLE1, involving variables D9 and E9.  The formula reference is a hyperlink -- you can click it to jump directly to the formula in question, where you can quickly see why it is a nonlinear function of D9 and E9.  The Premium Solver Platform's ability to diagnose your model can save you hours of time trying to find a problem by manual inspection!

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