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### qcp_vb.vb

' Copyright 2022, Gurobi Optimization, LLC

' This example formulates and solves the following simple QCP model:
'
'     maximize    x
'     subject to  x + y + z = 1
'                 x^2 + y^2 <= z^2 (second-order cone)
'                 x^2 <= yz        (rotated second-order cone)
'                 x, y, z non-negative

Imports Gurobi

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

' Create variables

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

' Set objective

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

' Add linear constraint: x + y + z = 1

model.AddConstr(x + y + z = 1.0, "c0")

' Add second-order cone: x^2 + y^2 <= z^2

model.AddQConstr(x * x + y * y <= z * z, "qc0")

' Add rotated cone: x^2 <= yz

model.AddQConstr(x * x <= y * z, "qc1")

' Optimize model

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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