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### bilinear_vb.vb

' Copyright 2023, Gurobi Optimization, LLC */

' This example formulates and solves the following simple bilinear model:
'
'     maximize    x
'     subject to  x + y + z <= 10
'                 x * y <= 2          (bilinear inequality)
'                 x * z + y * z == 1  (bilinear equality)
'                 x, y, z non-negative (x integral in second version)

Imports Gurobi

Class bilinear_vb
Shared Sub Main()
Try
Dim env As New GRBEnv("bilinear.log")
Dim model As New GRBModel(env)

' Create variables

Dim x As GRBVar = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "x")
Dim y As GRBVar = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "y")
Dim z As GRBVar = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "z")

' Set objective
Dim obj As GRBLinExpr = x
model.SetObjective(obj, GRB.MAXIMIZE)

' Add linear constraint: x + y + z <= 10

model.AddConstr(x + y + z <= 10, "c0")

' Add bilinear inequality: x * y <= 2

model.AddQConstr(x * y <= 2, "bilinear0")

' Add bilinear equality: x * z + y * z == 1

model.AddQConstr(x * z + y * z = 1, "bilinear1")

' Optimize model

Try
model.Optimize()
Catch e As GRBException
Console.WriteLine("Failed (as expected)")
End Try

model.Set(GRB.IntParam.NonConvex, 2)
model.Optimize()

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

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

x.Set(GRB.CharAttr.VType, GRB.INTEGER)
model.Optimize()

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

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

' Dispose of model and env

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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