Weak lower subdifferentiability in fractional programming

This paper considers generalized fractional programming problems for which numerators and denominators appearing in the objective function satisfy certain tangential convexity conditions ensuring its weak lower subdifferentiability. Estimates of the weak lower subdifferential in terms of the generalized subdifferentials of the numerators and denominators are provided and necessary and sufficient Karush-Kuhn-Tucker type optimality conditions involving these sets are obtained for problems with quasiconvex constraints.