Java Cplex Product of two Decision Variables

Question

Is there a way to get the product of two different decision variables in cplex java and add it to an objective function?

Ex.

decision variable -> x[i]

decision variable -> y[j]

-> x[i]*y[j]

Such a multiplikation should be possible, since it is still linear right?

Answer 1

Thanks to

@TimChippingtonDerrick ( https://stackoverflow.com/users/2108433/timchippingtonderrick )

and

@rkersh ( https://stackoverflow.com/users/1718477/rkersh )

I have found the answer to my problem.

At first such an objective function is not linear. This is the reason why for example

IloLinearNumExpr expressionName = cplex.linearNumExpr(); expressionName.addTerm(x[i],y[j]);

will not work, since such a multiplication is not being supported in a linear model. Only a variable with a coefficient can be added to such a linear expression.

For the second part, through the example provided by Cplex QPex1.java

I could write the product of two decision variables and add them to an objective function as in the following example:

IloNumExpr objective = cplex.numExpr();

for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
        objective = cplex.sum(objective,cplex.prod(y[i], z[j][i]));
    }
}
cplex.addMinimize(objective);