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.