Example 1: Bounded Least Squares

The nonlinear least-squares problem

\min \frac{1}{2}\sum\limits_{i = 0}^1 {f_i \left( x \right)^2 }

- 2 \le x_0 \le 0.5

-1 \le x_1 \le 2

where

f_0 (x) = 10(x_1 - x_0^2 ) \,\, {\rm{and}} \,\, f_1 (x) = (1 - x_0 )

is solved.

using System;
using Imsl.Math;

public class BoundedLeastSquaresEx1 : BoundedLeastSquares.IFunction
{
    public void F(double[] x, double[] f)
    {
        f[0] = 10.0 * (x[1] - x[0] * x[0]);
        f[1] = 1.0 - x[0];
    }

    public static void Main(String[] args)
    {
        int m = 2;
        int n = 2;
        int ibtype = 0;
        double[] xlb = new double[] { -2.0, -1.0 };
        double[] xub = new double[] { 0.5, 2.0 };

        BoundedLeastSquares.IFunction rosbck =
            new BoundedLeastSquaresEx1();
        BoundedLeastSquares zf =
            new BoundedLeastSquares(rosbck, m, n, ibtype, xlb, xub);
        zf.Solve();
        new PrintMatrix("Solution").Print(zf.GetSolution());
    }
}

Output

       Solution
           0          
0  0.5                
1  0.250000000009201
Link to C# source.