Try our new documentation site (beta).


piecewise_c++.cpp


/* Copyright 2021, 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;
}

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search

Gurobi Optimization