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piecewise_vb.vb
' Copyright 2023, 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
