Quasilower subdifferentiability and quasiconvex duality gap

In this note we introduce a notion of quasilower subdifferentiability which is an extension of that of lower subdifferentiability due to Plastria F. by using the concept of ε-subdifferential in convex analysis. We obtain that at a given point a function is quasilower subdifferentiable if and only if the values of this function and its second quasiconvex conjugate coincide. It is proved that the second quasiconvex conjugate is a best approximation in the class of second hα-conjugate defined by Martinez-Legaz and Romano-Rodriguez S. An application of the notion of quasilower subdifferentiability for the facial programming problems is given. (author). 10 refs