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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
