virtual Index get_number_of_nonlinear_variables()
This method is only important if the limited-memory quasi-Newton options is used, see Section 4.2. It is to be used to return the number of variables that appear nonlinearly in the objective function or in at least one constraint function. If a negative number is returned, IPOPT assumes that all variables are nonlinear.
If the user doesn't overload this method in her implementation of the class derived from TNLP, the default implementation returns -1, i.e., then all variables are assumed to be nonlinear.