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```ï»¿Imports System

Imports CenterSpace.NMath.Core
Imports CenterSpace.NMath.Analysis

Namespace CenterSpace.NMath.Core.Examples.VisualBasic

''' A .NET example in Visual Basic

' Example illustrating the use of the ActiveSetQPSolver Module to
' solve a Quadratic Programming (QP) problem.
Sub Main()

' Minimize q(x) = (x0 - 1)^2 + (x1 - 2.5)^2
' subject to -x0 + 2*x1 <= 2
'             x0 - 2*x1 >= -6
'            -x0 + 2*x1 >= -2
'                    x0 >= 0
'                    x1 >= 0

' Translating the objective function into the form
' 0.5*x'Hx + x'c
' yields
' H = | 2 0 |
'     | 0 2 |
'
' x = (-2 -5)
Dim H As New DoubleMatrix("2x2[2 0  0 2]")
Dim C As New DoubleVector(-2.0, -5.0)

' Set up the QP problem
Dim Problem As New QuadraticProgrammingProblem(H, C)
' add the lower bound of 0 for x0
' add the lower bound of 0 for x1

Dim solver As New ActiveSetQPSolver()

Console.WriteLine()

If (solver.Solve(Problem) <> True) Then
' Solver failed to find a solution. Print out the solver status.
Console.WriteLine("Solver failed. Status = {0}", solver.Status)
Return
End If

' Solver found a solution. Print out the optimal x and objective function
' values and the number of iterations.
Console.WriteLine("Solver found solution (x0, x1) = ({0}, {1}) after {2} iterations", _
solver.OptimalX(0), solver.OptimalX(1), solver.Iterations)
Console.WriteLine("Optimal objective function value = {0}", solver.OptimalObjectiveFunctionValue)

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