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### piecewise_vb.vb

' Copyright 2022, Gurobi Optimization, LLC

' This example considers the following separable, convex problem:
'
'    minimize    f(x) - y + g(z)
'    subject to  x + 2 y + 3 z <= 4
'                x +   y       >= 1
'                x,    y,    z <= 1
'
' where f(u) = exp(-u) and g(u) = 2 u^2 - 4 u, for all real u. It
' formulates and solves a simpler LP model by approximating f and
' g with piecewise-linear functions. Then it transforms the model
' into a MIP by negating the approximation for f, which corresponds
' to a non-convex piecewise-linear function, and solves it again.

Imports System
Imports Gurobi

Class piecewise_vb
Shared Function f(u As Double) As Double
Return Math.Exp(-u)
End Function
Shared Function g(u As Double) As Double
Return 2 * u * u - 4 * u
End Function

Shared Sub Main()
Try
' Create environment

Dim env As New GRBEnv()

' Create a new model

Dim model As New GRBModel(env)

' Create variables

Dim lb As Double = 0.0, ub As Double = 1.0

Dim x As GRBVar = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "x")
Dim y As GRBVar = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "y")
Dim z As GRBVar = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "z")

' Set objective for y

model.SetObjective(-y)

' Add piecewise-linear objective functions for x and z

Dim npts As Integer = 101
Dim ptu As Double() = New Double(npts - 1) {}
Dim ptf As Double() = New Double(npts - 1) {}
Dim ptg As Double() = New Double(npts - 1) {}

For i As Integer = 0 To npts - 1
ptu(i) = lb + (ub - lb) * i / (npts - 1)
ptf(i) = f(ptu(i))
ptg(i) = g(ptu(i))
Next

model.SetPWLObj(x, ptu, ptf)
model.SetPWLObj(z, ptu, ptg)

' Add constraint: x + 2 y + 3 z <= 4

model.AddConstr(x + 2 * y + 3 * z <= 4.0, "c0")

' Add constraint: x + y >= 1

model.AddConstr(x + y >= 1.0, "c1")

' Optimize model as an LP

model.Optimize()

Console.WriteLine("IsMIP: " & model.IsMIP)

Console.WriteLine(x.VarName & " " & x.X)
Console.WriteLine(y.VarName & " " & y.X)
Console.WriteLine(z.VarName & " " & z.X)

Console.WriteLine("Obj: " & model.ObjVal)

Console.WriteLine()

' Negate piecewise-linear objective function for x

For i As Integer = 0 To npts - 1
ptf(i) = -ptf(i)
Next

model.SetPWLObj(x, ptu, ptf)

' Optimize model as a MIP

model.Optimize()

Console.WriteLine("IsMIP: " & model.IsMIP)

Console.WriteLine(x.VarName & " " & x.X)
Console.WriteLine(y.VarName & " " & y.X)
Console.WriteLine(z.VarName & " " & z.X)

Console.WriteLine("Obj: " & model.ObjVal)

' Dispose of model and environment

model.Dispose()

env.Dispose()
Catch e As GRBException
Console.WriteLine("Error code: " + e.ErrorCode & ". " + e.Message)
End Try
End Sub
End Class


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