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QuickStart Samples

Quadratic Programming QuickStart Sample (Visual Basic)

Illustrates how to solve optimization problems a quadratic objective function and linear constraints using classes in the Extreme.Mathematics.Optimization namespace in Visual Basic.

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Option Infer On

' The quadratic programming classes reside in their own namespace.
Imports Extreme.Mathematics.Optimization
Imports Extreme.Mathematics

Namespace Extreme.Numerics.QuickStart.VB
    ' Illustrates solving quadratic programming problems
    ' using the classes in the Extreme.Mathematics.Optimization
    ' namespace of the Extreme Optimization Numerical Libraries for .NET.
    Module QuadraticProgramming

        Sub Main()
            ' This QuickStart illustrates the quadratic programming
            ' functionality by solving a portfolio optimization problem.

            ' Portfolio optimization is a common application of QP.
            ' For a collection of assets, the goal is to minimize
            ' the risk (variance of the return) while achieving
            ' a minimal return for a set maximum amount invested.

            ' The variables are the amounts invested in each asset.
            ' The quadratic term is the covariance matrix of the assets.
            ' THere is no linear term in this case.

            ' There are three ways to create a Quadratic Program.

            ' The first is in terms of matrices. The coefficients
            ' of the constraints and the quadratic terms are supplied 
            ' as matrices. The cost vector, right-hand side and 
            ' constraints on the variables are supplied as vectors.

            ' The linear term in the objective function:
            Dim c = Vector.CreateConstant(4, 0.0)
            ' The quaratic term in the objective function:
            Dim R = Matrix.CreateSymmetric(4,
                New Double() _
                     0.08, -0.05, -0.05, -0.05,
                    -0.05, 0.16, -0.02, -0.02,
                    -0.05, -0.02, 0.35, 0.06,
                    -0.05, -0.02, 0.06, 0.35
                }, MatrixTriangle.Upper, MatrixElementOrder.ColumnMajor)
            ' The coefficients of the constraints:
            Dim A = Matrix.Create(2, 4, New Double() _
            { _
                1, 1, 1, 1, _
                -0.05, 0.2, -0.15, -0.3 _
            }, MatrixElementOrder.RowMajor)
            ' The right-hand sides of the constraints:
            Dim b = Vector.Create(10000.0, -1000.0)

            ' We're now ready to call the constructor.
            ' The last parameter specifies the number of equality
            ' constraints.
            Dim qp1 As New QuadraticProgram(c, R, A, b, 0)

            ' Now we can call the Solve method to run the Revised
            ' Simplex algorithm:
            Dim x = qp1.Solve()
            Console.WriteLine("Solution: {0:F1}", x)
            ' The optimal value is returned by the Extremum property:
            Console.WriteLine("Optimal value:   {0:F1}", qp1.OptimalValue)

            ' The second way to create a Quadratic Program is by constructing
            ' it by hand. We start with an 'empty' quadratic program.
            Dim qp2 As New QuadraticProgram()

            ' Next, we add two variables: we specify the name, the cost,
            ' and optionally the lower and upper bound.
            qp2.AddVariable("X1", 0.0)
            qp2.AddVariable("X2", 0.0)
            qp2.AddVariable("X3", 0.0)
            qp2.AddVariable("X4", 0.0)

            ' Next, we add constraints. Constraints also have a name.
            ' We also specify the coefficients of the variables,
            ' the lower bound and the upper bound.
            Dim c1Values = Vector.Create(1.0, 1.0, 1.0, 1.0)
            qp2.AddLinearConstraint("C1", c1Values, ConstraintType.LessThanOrEqual, 10000)
            Dim c2Values = Vector.Create(0.05, -0.2, 0.15, 0.3)
            qp2.AddLinearConstraint("C2", c2Values, ConstraintType.GreaterThanOrEqual, 1000)
            ' If a constraint is a simple equality or inequality constraint,
            ' you can supply a QuadraticProgramConstraintType value and the
            ' right-hand side of the constraint.

            ' Quadratic terms must be set individually.
            ' Each combination appears at most once.
            qp2.SetQuadraticCoefficient("X1", "X1", 0.08)
            qp2.SetQuadraticCoefficient("X1", "X2", -0.05 * 2)
            qp2.SetQuadraticCoefficient("X1", "X3", -0.05 * 2)
            qp2.SetQuadraticCoefficient("X1", "X4", -0.05 * 2)
            qp2.SetQuadraticCoefficient("X2", "X2", 0.16)
            qp2.SetQuadraticCoefficient("X2", "X3", -0.02 * 2)
            qp2.SetQuadraticCoefficient("X2", "X4", -0.02 * 2)
            qp2.SetQuadraticCoefficient("X3", "X3", 0.35)
            qp2.SetQuadraticCoefficient("X3", "X4", 0.06 * 2)
            qp2.SetQuadraticCoefficient("X4", "X4", 0.35)

            ' We can now solve the quadratic program:
            x = qp2.Solve()
            Console.WriteLine("Solution: {0:F1}", x)
            Console.WriteLine("Optimal value:   {0:F1}", qp2.OptimalValue)

            ' Finally, we can create a quadratic program from an MPS file.
            ' The MPS format is a standard format.
            Dim qp3 = MpsReader.ReadQuadraticProgram("..\..\..\..\data\portfolio.qps")
            ' We can go straight to solving the quadratic program:
            x = qp3.Solve()
            Console.WriteLine("Solution: {0:F1}", x)
            Console.WriteLine("Optimal value:   {0:F1}", qp3.OptimalValue)

            Console.Write("Press Enter key to exit...")
        End Sub

    End Module

End Namespace