# Documentation

Filter Content By
Version
Languages

### piecewise_c++.cpp

```/* Copyright 2019, Gurobi Optimization, LLC */

/* This example considers the following separable, convex problem:

minimize    f(x) - y + g(z)
subject to  x + 2 y + 3 z <= 4
x +   y       >= 1
x,    y,    z <= 1

where f(u) = exp(-u) and g(u) = 2 u^2 - 4 u, for all real u. It
formulates and solves a simpler LP model by approximating f and
g with piecewise-linear functions. Then it transforms the model
into a MIP by negating the approximation for f, which corresponds
to a non-convex piecewise-linear function, and solves it again.
*/

#include "gurobi_c++.h"
#include <cmath>
using namespace std;

double f(double u) { return exp(-u); }
double g(double u) { return 2 * u * u - 4 * u; }

int
main(int   argc,
char *argv[])
{
double *ptu = NULL;
double *ptf = NULL;
double *ptg = NULL;

try {

// Create environment

GRBEnv env = GRBEnv();

// Create a new model

GRBModel model = GRBModel(env);

// Create variables

double lb = 0.0, ub = 1.0;

GRBVar x = model.addVar(lb, ub, 0.0, GRB_CONTINUOUS, "x");
GRBVar y = model.addVar(lb, ub, 0.0, GRB_CONTINUOUS, "y");
GRBVar z = model.addVar(lb, ub, 0.0, GRB_CONTINUOUS, "z");

// Set objective for y

model.setObjective(-y);

// Add piecewise-linear objective functions for x and z

int npts = 101;
ptu = new double[npts];
ptf = new double[npts];
ptg = new double[npts];

for (int i = 0; i < npts; i++) {
ptu[i] = lb + (ub - lb) * i / (npts - 1);
ptf[i] = f(ptu[i]);
ptg[i] = g(ptu[i]);
}

model.setPWLObj(x, npts, ptu, ptf);
model.setPWLObj(z, npts, ptu, ptg);

// Add constraint: x + 2 y + 3 z <= 4

model.addConstr(x + 2 * y + 3 * z <= 4, "c0");

// Add constraint: x + y >= 1

model.addConstr(x + y >= 1, "c1");

// Optimize model as an LP

model.optimize();

cout << "IsMIP: " << model.get(GRB_IntAttr_IsMIP) << endl;

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;

cout << endl;

// Negate piecewise-linear objective function for x

for (int i = 0; i < npts; i++) {
ptf[i] = -ptf[i];
}

model.setPWLObj(x, npts, ptu, ptf);

// Optimize model as a MIP

model.optimize();

cout << "IsMIP: " << model.get(GRB_IntAttr_IsMIP) << endl;

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;
}

delete[] ptu;
delete[] ptf;
delete[] ptg;

return 0;
}
```