C# Trust Region Minimization Example

using System;
using System.Collections.Generic;
using System.Text;

using CenterSpace.NMath.Core;
using CenterSpace.NMath.Analysis;

namespace TrustRegionMinimizationExample
{
  class TrustRegionMinimizationExample
  {
    /// <summary>
    /// A .NET example in C# showing how to minimize a function using the Trust Region 
    /// method.
    /// </summary>
    static void Main(string[] args)
    {
      Console.WriteLine();

      // Minimization in this context means finding the solution that evaluates to the vector with the smallest
      // two norm (distance from origin).

      // Wrap the function to minimize in a delegate. MyFunction() that has three input variables and four 
      // output variables
      NMathFunctions.DoubleVectorDoubleVectorFunction f = new NMathFunctions.DoubleVectorDoubleVectorFunction(MyFunction);
      int ydim = 4;

      // Choose a starting point
      DoubleVector start = new DoubleVector(50.0, 30.0, -1000.0);

      // Create a minimizer with default tolerance and maximum iterations.
      TrustRegionMinimizer minimizer = new TrustRegionMinimizer();

      // Compute the solution and display the results.
      DoubleVector solution = minimizer.Minimize(f, start, ydim);
      Console.WriteLine("The minimizer started at ");
      Console.WriteLine(start);
      Console.WriteLine("with a residual of " + minimizer.InitialResidual);
      Console.WriteLine();
      Console.WriteLine("After " + minimizer.Iterations + " iterations, it reached a solution at");
      Console.WriteLine(solution);
      Console.WriteLine("with a residual of " + minimizer.FinalResidual);
      Console.WriteLine();
      Console.WriteLine("It stopped because " + minimizer.StopCriterion + ".");

      // Add some constraints. Set a lower bound to (0, 0, 0) and an upper bound to (10, 10, 10)
      DoubleVector lowerBounds = new DoubleVector(3);
      DoubleVector upperBounds = new DoubleVector(3, 10.0);

      // Minimize again, and display the result.
      solution = minimizer.Minimize(f, start, ydim, lowerBounds, upperBounds);
      Console.WriteLine();
      Console.WriteLine("Lower bounds = " + lowerBounds);
      Console.WriteLine("Upper bounds = " + upperBounds);
      Console.WriteLine("The solution is at");
      Console.WriteLine(solution);
      Console.WriteLine("with a residual of " + minimizer.FinalResidual);

      Console.WriteLine();
      Console.WriteLine("Press Enter Key");
      Console.Read();

    }  // Main

    // The function to minimize
    private static DoubleVector MyFunction(DoubleVector x)
    {
      DoubleVector y = new DoubleVector(4);
      y[0] = 5 * x[1] * x[1] + x[2] * x[2];
      y[1] = 4 * x[0] * x[0] - x[2] * x[2] + 45;
      y[2] = x[0] * 3 * x[0] - x[1] * x[1] + 9;
      y[3] = y[0] + y[1] + y[2] * y[2] - 43;
      return y;
    }
  }
}