Simplex Method. The banana function.

The Simplex class is used to minimizes a function of several variables by using the Nelder-Mead (Simplex) method. This class can be used for unconstrained and bounded constrained minimization.

 In this example the Simplex class is used to solve the banana function problem:

            f(a,b)=100*(b-a^2)^2+(1-a)^2
            The minimum is at (1,1) and the  function value is 0.

C# Code

 using DotNumerics.Optimization;

public void OptimizationSimplex()

{

    Simplex simplex = new Simplex();

    double[] initialGuess = new double[2];

    initialGuess[0] = 0.1;

    initialGuess[1] = 2;

    double[] minimum = simplex.ComputeMin(BananaFunction, initialGuess);

}

//f(a,b) = 100*(b-a^2)^2 + (1-a)^2

private double BananaFunction(double[] x)

{

    double f = 0;

    f = 100 * Math.Pow((x[1] - x[0] * x[0]), 2) + Math.Pow((1 - x[0]), 2);

    return f;

}

Solution

Simplex Method.
a = 0.999999997960522,   b = 0.999999995617332