Variational Subdifferential for Quasiconvex Functions

It is shown that a convenient subdifferential for the class of quasiconvex functions is variational. This property combines a variational principle with a kind of weak fuzzy sum rule. It entails a number of useful properties. The subdifferential considered here is the lower subdifferential at the origin (in the sense of Plastria) of the incident derivative or inner epiderivative of the function.