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### qcp_cs.cs

/* Copyright 2020, 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
*/

using System;
using Gurobi;

class qcp_cs
{
static void Main()
{
try {
GRBEnv    env   = new GRBEnv("qcp.log");
GRBModel  model = new GRBModel(env);

// Create variables

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

// Set objective

GRBLinExpr obj = 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

// 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 (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message);
}
}
}