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### bilinear_c++.cpp

/* Copyright 2021, 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)
*/
#include <cassert>
#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 <= 10

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

// Add bilinear inequality constraint: x * y <= 2

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

// Add bilinear equality constraint: y * z == 1

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

// First optimize() call will fail - need to set NonConvex to 2

try {
model.optimize();
assert(0);
} catch (GRBException e) {
cout << "Failed (as expected)" << endl;
}

model.set(GRB_IntParam_NonConvex, 2);
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;

// Constrain x to be integral and solve again
x.set(GRB_CharAttr_VType, GRB_INTEGER);
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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