Example: iloqpex1.cpp

This example is almost identical to ilolpex1.cpp with only function populatebyrow to create the model. Also, this function differs only in the creation of the objective from its ilolpex1.cpp counterpart. Here the objective function is created and added to the model like this:

model.add(IloMaximize(env, x[0] + 2 * x[1] + 3 * x[2]
              - 0.5 * (33*x[0]*x[0] + 22*x[1]*x[1] + 11*x[2]*x[2]
                            - 12*x[0]*x[1] - 23*x[1]*x[2]) ));

In general, any expression built of basic operations +, -, *, / constant, and brackets '()' that amounts to a quadratic and optional linear term can be used for building QP objective function. Note that the expressions of the objective or any constraint of the model must not contain IloPiecewiselinear when a QP objective is specified, in order for IloCplex to be able to process the model.

Complete Program: iloqpex1.cpp

The complete program, iloqpex1.cpp, appears here or online in the standard distribution.

#include <ilcplex/ilocplex.h>
ILOSTLBEGIN

static void
   populatebyrow     (IloModel model, IloNumVarArray var, IloRangeArray con);

int
main (int argc, char **argv)
{
   IloEnv   env;
   try {
      IloModel model(env);
      IloNumVarArray var(env);
      IloRangeArray con(env);

      populatebyrow (model, var, con);

      IloCplex cplex(model);

      // Optimize the problem and obtain solution.
      if ( !cplex.solve() ) {
         env.error() << "Failed to optimize LP" << endl;
         throw(-1);
      }

      IloNumArray vals(env);
      env.out() << "Solution status = " << cplex.getStatus() << endl;
      env.out() << "Solution value  = " << cplex.getObjValue() << endl;
      cplex.getValues(vals, var);
      env.out() << "Values        = " << vals << endl;
      cplex.getSlacks(vals, con);
      env.out() << "Slacks        = " << vals << endl;
      cplex.getDuals(vals, con);
      env.out() << "Duals         = " << vals << endl;
      cplex.getReducedCosts(vals, var);
      env.out() << "Reduced Costs = " << vals << endl;

      cplex.exportModel("qpex1.lp");
   }
   catch (IloException& e) {
      cerr << "Concert exception caught: " << e << endl;
   }
   catch (...) {
      cerr << "Unknown exception caught" << endl;
   }

   env.end();

   return 0;
}  // END main


// To populate by row, we first create the variables, and then use them to
// create the range constraints and objective.  The model we create is:
//
//    Maximize
//     obj: x1 + 2 x2 + 3 x3
//            - 0.5 ( 33*x1*x1 + 22*x2*x2 + 11*x3*x3
//                             - 12*x1*x2 - 23*x2*x3 )
//    Subject To
//     c1: - x1 + x2 + x3 <= 20
//     c2: x1 - 3 x2 + x3 <= 30
//    Bounds
//     0 <= x1 <= 40
//    End

static void
populatebyrow (IloModel model, IloNumVarArray x, IloRangeArray c)
{
   IloEnv env = model.getEnv();

   x.add(IloNumVar(env, 0.0, 40.0));
   x.add(IloNumVar(env));
   x.add(IloNumVar(env));
   model.add(IloMaximize(env, x[0] + 2 * x[1] + 3 * x[2]
                            - 0.5 * (33*x[0]*x[0] + 22*x[1]*x[1] + 11*x[2]*x[2]
                                                  - 12*x[0]*x[1] - 
23*x[1]*x[2]) ));

   c.add( - x[0] +     x[1] + x[2] <= 20);
   c.add(   x[0] - 3 * x[1] + x[2] <= 30);
   model.add(c);

}  // END populatebyrow