VB Multi Variable Minimization Example

Imports System

Imports CenterSpace.NMath.Core


Namespace CenterSpace.NMath.Examples.VisualBasic

  A .NET example in Visual Basic showing how to use the multivariable minimizer.
  Module MultiVariableMinimizationExample

    Private Function df0(ByVal X As DoubleVector) As Double
      Return 1.6 * Math.Pow(X(0), 3)
    End Function

    Private Function df1(ByVal X As DoubleVector) As Double
      Return 0.1 * Math.Cos(X(1))
    End Function

    Private Function df2(ByVal X As DoubleVector) As Double
      Return 10 * X(2)
    End Function

    Private Function df3(ByVal X As DoubleVector) As Double
      Return 16 * Math.Pow(X(3), 3)
    End Function

    Private Function F(ByVal x As DoubleVector) As Double
      Return 0.4 * Math.Pow(x(0), 4) + 0.1 * Math.Sin(x(1)) + 5 * x(2) * x(2) + 4 * Math.Pow(x(3), 4)
    End Function

    Sub Main()

      Create a multivariable function.
      Dim D As Func(Of DoubleVector, Double) = AddressOf F
      Dim Func As New MultiVariableFunction(D)

      Start at ( 0, 0, 0, 0 ).
      Dim StartPoint As New DoubleVector(0.0, 0.0, 0.0, 0.0)

      Create a DownhillSimplexMinimizer with the default error tolerance and maximum
      iterations.
      Dim Simplex As New DownhillSimplexMinimizer

      Minimize the function.
      Dim Min As DoubleVector = Simplex.Minimize(Func, StartPoint)

      Console.WriteLine()

      Console.WriteLine("DownhillSimplexMinimizer found a minimum of " & Func.Evaluate(Min))
      Console.WriteLine("at " & Min.ToString("G7") & ".")

      If (Simplex.ToleranceMet) Then
        Error is less than desired tolerance
        Console.Write("Error of " & Simplex.Error & " is within tolerance of ")
        Console.WriteLine(Simplex.Tolerance & ".")
      Else
        Minimization ended because maximum iterations was reached
        Console.WriteLine("Ended with maximum iterations.")
      End If
      Console.WriteLine()

      Increase the maximum number of iterations from the default of 100 to 1000.
      Simplex.MaxIterations = 1000

      Minimize the function.
      Min = Simplex.Minimize(Func, StartPoint)

      Console.WriteLine("DownhillSimplexMinimizer found a minimum of " & Func.Evaluate(Min))
      Console.WriteLine("at " & Min.ToString("G7") & ".")

      If (Simplex.ToleranceMet) Then
        Error is less than desired tolerance
        Console.Write("Error of " & Simplex.Error & " is within tolerance of ")
        Console.WriteLine(Simplex.Tolerance & ".")
      Else
        Minimization ended because maximum iterations was reached
        Console.WriteLine("Ended with maximum iterations.")
      End If
      Console.WriteLine()

      Now try using Powells Method.

      Create the minimizer with default error tolerance and default maximum iterations.
      Dim Powell As New PowellMinimizer

      Perform the minimization.
      Min = Powell.Minimize(Func, StartPoint)

      Console.WriteLine("PowellMinimizer found a minimum of " & Func.Evaluate(Min))
      Console.WriteLine("at " & Min.ToString("G7") & ".")

      If (Powell.ToleranceMet) Then
        Error is less than desired tolerance
        Console.Write("Error of " & Powell.Error & " is within tolerance of ")
        Console.WriteLine(Powell.Tolerance & ".")
      Else
        Minimization ended because maximum iterations was reached
        Console.WriteLine("Ended with maximum iterations.")
      End If
      Console.WriteLine()

      If the derivatives are known, then use one of the IMultiVariableDMinimizer
      classes such as ConjugateGradientMinimizer.

      Create an array of partial derivatives
      Dim Partials(3) As MultiVariableFunction
      Partials(0) = New MultiVariableFunction(New Func(Of DoubleVector, Double)(AddressOf df0))
      Partials(1) = New MultiVariableFunction(New Func(Of DoubleVector, Double)(AddressOf df1))
      Partials(2) = New MultiVariableFunction(New Func(Of DoubleVector, Double)(AddressOf df2))
      Partials(3) = New MultiVariableFunction(New Func(Of DoubleVector, Double)(AddressOf df3))

      Create the minimizer with default tolerance and default maximum iterations.
      Dim CG As New ConjugateGradientMinimizer

      Perform the minimization.
      StartPoint = New DoubleVector(1.0, 2.0, 3.0, 4.0)
      Min = CG.Minimize(Func, Partials, StartPoint)

      Console.WriteLine("ConjugateGradientMinimizer found a minimum of " & Func.Evaluate(Min))
      Console.WriteLine("at " & Min.ToString("G7") & ".")

      If (CG.ToleranceMet) Then
        Error is less than desired tolerance
        Console.Write("Error of " & CG.Error & " is within tolerance of ")
        Console.WriteLine(CG.Tolerance & ".")
      Else
        Minimization ended because maximum iterations was reached
        Console.WriteLine("Ended with maximum iterations.")
      End If
      Console.WriteLine()

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

    End Sub


  End Module

End Namespace