The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method in .NET (C# and Visual Basic)
The BFGS routine optimizes a scalar function without constaints. In contrast to the Newton method it utilizes an approximation to the second derivative matrix, the Hessian. For more details please see the Wikipedia article.
A simple Example for the BFGS method
Here is a simple example with a quadratic function.