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### qcp_c++.cpp

/* 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
*/

#include "gurobi_c++.h"
using namespace std;

int
main(int   argc,
char *argv[])
{
try {
GRBEnv env = GRBEnv();

GRBModel model = 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, "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();

cout << x.get(GRB_StringAttr_VarName) << " "
<< x.get(GRB_DoubleAttr_X) << endl;
cout << y.get(GRB_StringAttr_VarName) << " "
<< y.get(GRB_DoubleAttr_X) << endl;
cout << z.get(GRB_StringAttr_VarName) << " "
<< z.get(GRB_DoubleAttr_X) << endl;

cout << "Obj: " << model.get(GRB_DoubleAttr_ObjVal) << endl;

} catch(GRBException e) {
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
} catch(...) {
cout << "Exception during optimization" << endl;
}

return 0;
}


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