VB Constrained Least Squares Example

Imports System

Imports CenterSpace.NMath.Core


Namespace CenterSpace.NMath.Examples.VisualBasic

  <summary>
  A .NET example in Visual Basic showing how to use ConstrainedLeastSquares class to
  solve the constrained least squares problem
  Cx = d, subject to the constraints
  Ax &lt b
  </summary>
  Public Module ConstrainedLeastSquaresExample

    Sub Main()

      Solve, in the least squares sense, Cx = d, subject to Ax <= b 
      and -0.1 <= x[i] <= 2.0
      Dim C As New DoubleMatrix("5x4 [0.9501    0.7620    0.6153    0.4057 " &
                                              "0.2311    0.4564    0.7919    0.9354 " &
                                              "0.6068    0.0185    0.9218    0.9169 " &
                                              "0.4859    0.8214    0.7382    0.4102 " &
                                              "0.8912    0.4447    0.1762    0.8936]")

      Dim D As New DoubleVector(0.0578, 0.3528, 0.8131, 0.0098, 0.1388)

      Constraint coefficient matrix
      Dim A As New DoubleMatrix("3x4[0.2027    0.2721    0.7467    0.4659 " &
                                             "0.1987    0.1988    0.4450    0.4186 " &
                                             "0.6037    0.0152    0.9318    0.8462]")

      Constraints right hand sides.
      Dim B As New DoubleVector(0.5251, 0.2026, 0.6721)

      Create the constrained least squares problem for minimizing
      || Cx - d||^2 subject to Ax <= b and -0.1 <= x[i] <= 2.0
      We first construct the problem object from the matrix C and the
      vector d, we then add the constraints.
      Dim Problem = New ConstrainedLeastSquaresProblem(C, D)

      Add the inequality constraints Ax <= b using a constraint tolerance
      of 0.00001. This allows for small violations of the constraints. 
      Specifically the constraints will be considered satisfied for a 
      vector x if
      Ax <= b + 0.00001
      Dim ConstraintTolerance As Double = 0.00001

      Dim I As Integer
      For I = 0 To A.Rows - 1
        Problem.AddUpperBoundConstraint(A.Row(I), B(I), ConstraintTolerance)
      Next

      All variable values for the solution must satisfy the bounds
      -0.1 <= x[i] <= 2.0
      Dim LB As New DoubleVector(Problem.NumVariables, -0.1)
      Dim UB As New DoubleVector(Problem.NumVariables, 2.0)
      For I = 0 To Problem.NumVariables - 1
        Problem.AddBounds(I, LB(I), UB(I), 0.00001)
      Next

      Create the solver instance.
      Dim Solver As New ConstrainedLeastSquares()

      The ConstrainedLeastSquares solver uses a QP (Quadratic Programming) solver
      to solve the constrained least squares problem.
      The current default QP solver is the NMath active set quadratic programming
      solver with default options.
      Dim Success As Boolean = Solver.Solve(Problem)
      Console.WriteLine("Default solver success = " & Success)
      Console.WriteLine("Default solver solution x = " & Solver.X.ToString("0.0000"))
      Console.WriteLine("Default solver residual norm = " & Solver.ResidualNorm.ToString("0.0000"))
      Console.WriteLine("Default solver performed {0} iterations", solver.Iterations)

      You can pass in an instance of a quadratic programming solver for the 
      constrained least squares class to use. This allows you to set 
      option on the QP solver and inspect results of the QP
      solver.
      Dim InteriorPointQP As New InteriorPointQPSolver()
      Dim SolverParams As New InteriorPointQPSolverParams()
      SolverParams.MaxIterations = 10000
      SolverParams.PresolveLevel = InteriorPointQPSolverParams.PresolveLevelOption.None
      Solver.Solve(Problem, InteriorPointQP, SolverParams)
      Console.WriteLine()
      Console.WriteLine("Interior point solver success = " & Success)
      Console.WriteLine("Interior point QP result = " & InteriorPointQP.Result)
      Console.WriteLine("Interior point QP solver iteration count = " & Solver.Iterations)
      Console.WriteLine("Interior point solver solution x = " & Solver.X.ToString("0.0000"))
      Console.WriteLine("Interior point solver residual norm = " & Solver.ResidualNorm.ToString("0.0000"))

      If you use the active set QP solver you can determine which constraints
      are active in the solution by accessing the active set QP solvers 
      Lagrange multiplier property. A constraint is active if its corresponding
      Lagrange multiplier is nonzero.
      Dim ActiveSetQP As New ActiveSetQPSolver()
      Success = Solver.Solve(Problem, ActiveSetQP)
      Console.WriteLine()
      Console.WriteLine("Active set solver success = " & Success)
      Console.WriteLine("Active set solver solution x = " & Solver.X.ToString("0.0000"))
      Console.WriteLine("Active set solver residual norm = " & Solver.ResidualNorm.ToString("0.0000"))
      Print out the active constraints.
      For I = 0 To ActiveSetQP.LagrangeMultiplier.Length - 1
        If (ActiveSetQP.LagrangeMultiplier(I) <> 0.0) Then
          Console.WriteLine("Constraint {0} = {1} is active", I, Problem.Constraints(I).ToString())
        End If
      Next

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

    End Sub
  End Module
End Namespace