Is it possible to solve mixed-integer non-linear programming (MINLP) problem with CPLEX?

Question

I am trying to solve a mixed integer non-linear programming (MINLP) problem. I am aware that CPLEX can solve a mixed integer quadratic programming (MIQP) problem where the objective function contains a quadratic formula (the product of at most two decision variables).

However, my MINLP has the objective function which is the product of more than three integer decision variables, and all constraints are linear. I would like to know that can CPLEX solve this kind of the MINLP problem?

Thank you.

Answer 1

This type of problem can not be solved using CPLEX or docplex. If you want to use these tools for your model then your only option is to reformulate your objective function. You may for example consider formulating the objective as a piecewise linear function.

Sometimes those products of multiple variables can be linearized. For example, the product of three binary variables is 1 if and only if all the variables are 1. This can be expressed by introducing a new variable that represents the product and constraints that force the variable to 1 if all binaries are 1 and to 0 otherwise. Similar things can be done in other cases.