You may often find it useful to design a model of your problem that organizes the unknowns into arrays of variables. Concert Technology provides a class of arrays for numerical variables, IloNumVarArray.

Let's assume two constrained floating-point variables, x and y, and one constrained integer variable, k. These three variables use the following intervals as their domains:

x [-5, 108]

y [0, 108]

k [-1000, 1000]

Let's also assume the following system of equations must be solved:

x3 + 10x = yx - 2k

kx + 7.7y = 2.4

(k - 1)y+1 10

(log(y + 2x + 12.) k + 5. y k2) (x 0. y 1)

x 0 k > 3

The solution is:

x = -1.285057857952

y = 0.9792508352872

k = 4

The complete program follows:

#include <ilsolver/ilosolverfloat.h>
 
ILOSTLBEGIN
 
int main(){    
  IloEnv env;
  try {
    IloModel model(env);
 
    IloNumVar x(env, -5, 1e8);
    IloNumVar y(env, 0, 1e8);
    IloIntVar k(env, -1000, 1000);
 
    model.add(IloPower(x,3) + 10*x == IloPower(y, x) - IloPower(2, k));
    model.add(k*x + 7.7*y == 2.4);
    model.add(IloPower(k-1, y+1) <= 10);
    model.add(IloIfThen(env, IloLog(y + 2*x + 12) <= k + 5 || y >= k*k, x <= 0 && y <= 1));
    model.add(IloIfThen(env, x <= 0, k > 3));
 
    IloNumVarArray vars(env, 2, x, y);
    IloSolver solver(env);
 
    solver.out().precision(16);
 
    solver.extract(model);
 
    if (solver.solve(IloGenerateBounds(env, vars, .1))) {
      solver.out() << "x = " <<  solver.getFloatVar(x) << endl;
      solver.out() << "y = " <<  solver.getFloatVar(y) << endl;
      solver.out() << "k = " <<  solver.getIntVar(k) << endl;
    }
    solver.printInformation();
  }
  catch (IloException& ex) {
    cout << "Error: " << ex << endl;
  }
  env.end();
  return 0;
}
 
 

Here's the output of the program.

x = [-1.285057857942743..-1.285057857928474]
y = [0.9792508352918879..0.979250835302613]
k = [4]

The complete program is available online in the YourSolverHome/examples/src/narin.cpp file.