Abstract
An axiomatic approach of normal operators to sublevel sets is given. Considering the Clarke-Rockafellar subdifferential (resp. quasiconvex functions), the definition given in [4] (resp. [5]) is recovered. Moreover, the results obtained in [4] are extended in this more general setting. Under mild assumptions, quasiconvex continuous functions are classified, establishing an equivalence relation between functions with the same normal operator. Applications in pseudoconvexity are also discussed.
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Aussel, D., Daniilidis, A. (2001). Normal Cones to Sublevel Sets: An Axiomatic Approach. In: Hadjisavvas, N., Martínez-Legaz, J.E., Penot, JP. (eds) Generalized Convexity and Generalized Monotonicity. Lecture Notes in Economics and Mathematical Systems, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56645-5_5
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DOI: https://doi.org/10.1007/978-3-642-56645-5_5
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