Abstract: In the case when the functions are not necessarily lower semicontinous and the sets are not necessarily closed, the fractional optimization problem is turned into a constraint optimization problem with Dinkelbach method. With the properties of ε-subdifferentials, some new constraint qualifications are introduced and some characteristic characterizations of ε-optimal solutions are established.

Key words: fractional optimization problem, constraint optimization problem, Dinkelbach method, constraint qualification, approximate optimality condition