Originally posted by: SystemAdmin

Hello!

I'm solving a minimization problem using cplex java. I declare the objective function as linearNumExpression, but one of the terms requires the multiplication of two decision variables, so it becomes quadratic. My problem is that if I decplare the objective function as quadratic the rest of the terms that are linear are not working. Have you got any idea how I can overcome this problem? In other words how to use linear and quadratic terms together in the objective function?

Thanks
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Originally posted by: SystemAdmin

You can use IloNumExpr instead of IloLinearNumExpr. The former allows any kind of terms in it. Or collect the quadratic terms in an instance of IloQuadNumExpr and in the end use cplex.sum() to add the linear expression and the quadratic expression.
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Originally posted by: SystemAdmin

Thanks for the quick answer!
If I use IloNumExpr I cannot use the addTerm. When you say to use cplex.sum() how exactly do you mean it? I provide you with the relevant part of my code

IloLinearNumExpr obj_func = cplex.linearNumExpr();

for(i = 0; i < numVs; i++)
{
for(j=0; j<numPs; j++)
{
obj_func.addTerm((0.2*tDriving[i][j]), y[i][j]); // y is a decision variable, tDriving is a double java variable
}
}

for(j=0; j<numPs; j++)
{

for(i=0;i<numVs; i++)
{
IloQuadNumExpr p = cplex.quadNumExpr();
for(int ii=0; ii<numEVs; ii++)
{
for (k=0; k<100; k++)
{
p.addTerm(1, n[j][k]ii,y[i][j]); // n is the second decision variable
}
}
obj_func.add(p);
}
}
cplex.addMinimize(obj_func);
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Originally posted by: SystemAdmin

I think this should work:

IloLinearNumExpr lin = cplex.linearNumExpr();
 
for(i = 0; i < numVs; i++) {
  for(j=0; j<numPs; j++) {
    lin.addTerm((0.2*tDriving[i][j]), y[i][j]);
  }
}
 
IloQuadNumExpr quad = cplex.quadNumExpr();
for(j=0; j<numPs; j++) {
  for(i=0;i<numVs; i++) {
    for(int ii=0; ii<numEVs; ii++) {
      for (k=0; k<100; k++) {
        quad.addTerm(1, n[j][k]ii,y[i][j]);
      }
    }
  }
}
cplex.addMinimize(cplex.sum(lin, quad));

Please also refer to the QPex1.java, QPex2.java, and QPex3.java examples in the CPLEX distribution. They illustrate how to compose a quadratic objective function.
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Originally posted by: SystemAdmin

Thanks a lot Daniel! This works!
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