Abstract
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.
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Penot, J.P. Variational Subdifferential for Quasiconvex Functions. Journal of Optimization Theory and Applications 111, 165–171 (2001). https://doi.org/10.1023/A:1017579516340
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DOI: https://doi.org/10.1023/A:1017579516340