Solving a general nonlinear programming problem

Example 1: Solving a general nonlinear programming problem

A general nonlinear programming problem is solved using a finite difference gradient. The problem

${\rm {min}} \,\, F(x) = (x_1 - 2)^2 + (x_2 - 1)^2$

subject to

$g_2(x) = -x_1^2 / 4 - x_2^2 + 1 \ge 0$

is solved.

using System;
using Imsl.Math;

public class MinConNLPEx1 : MinConNLP.IFunction
{
    public double F(double[] x, int iact, bool[] ierr)
    {
        double result;
        ierr[0] = false;
        if (iact == 0)
        {
            result = (x[0] - 2.0) * (x[0] - 2e0) + 
                (x[1] - 1.0) * (x[1] - 1.0);
            return result;
        }
        else
        {
            switch (iact)
            {
                
                case 1: 
                    result = (x[0] - 2.0 * x[1] + 1.0);
                    return result;
                
                case 2: 
                    result = (-(x[0] * x[0]) / 4.0 - (x[1] * x[1])
                        + 1.0);
                    return result;
                
                default: 
                    ierr[0] = true;
                    return 0.0;
                
            }
        }
    }
    

    public static void  Main(String[] args)
    {
        int m = 2;
        int me = 1;
        int n = 2;
        MinConNLP minconnon = new MinConNLP(m, me, n);
        minconnon.SetGuess(new double[]{2.0, 2.0});
        double[] x = minconnon.Solve(new MinConNLPEx1());
        new PrintMatrix("x").Print(x);
    }
}

Output

          x
           0          
0  0.822875655532512  
1  0.911437827766256

Link to C# source.