ILNumerics - Technical Computing Tools

High Performance Framework for Visualization

and Computing in Industry and Science



ILNumerics® Optimization Toolbox - Quick Start Guide

This quick start guide will help you to get up and running with common optimization problems. Consult the subsequent chapters of the online documentation for more in-depth information.

Optimization of a Function with two Variables

Consider the following function as an example of a common optimization problem:$$f = e^{0.001 (y^2 + (x - 2)^2)}$$


ILNumerics.Optimization.fmin() finds the minimum of this function at [2,0]. This is the global minimum, since the function has only one minimum:


We allow a solution in the whole definition space (R2). No restriction (constraint) exists. Therefore, this problem is an unconstrained optimization problem. Read more about handling unconstrained problems here: Unconstrained Optimization.

The objective function has a single return value. In general, finding the minimum of such problems involves two main steps:

  1. Implement the objective function.
  2. Specify a starting point to begin searching for the minimum.

Constrained Optimization

Let's suppose that for some reasons the optimal solution for the above problem would be restricted to the subspace of R2 having an x coordinate larger than 3.0 and an y coordinate larger than -1. We can find the minimum of such constrained optimization problem with the same fmin() function:

Similarly, upper bounds for each dimension can be specified using the upperBound parameter. The constrained solver is capable of handling bound constraints, equalty and inequalty constraints.

Read more here: Constrained Optimization

Nonlinear Least Squares Optimization

Maybe the most popular application for nonlinear least square problems is data fitting. The following complete example fits a polynomial model to data values created from a sinosoidal function (with some noise). The example is also found in the example projects section.

Output created:

Optimization Toolbox in .NET (C# and Visual Basic)

Read more about Nonlinear Least Squares methods in ILNumerics.

ILNumerics Optimization Toolbox is available for individual purchase.