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Are Generalized Derivatives Sseful for Generalized Convex Functions?

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Generalized Convexity, Generalized Monotonicity: Recent Results

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 27))

Abstract

We present a review of some ad hoc subdifferentials which have been devised for the needs of generalized convexity such as the quasi-subdifferentials of Greenberg-Pierskalla, the tangential of Crouzeix, the lower subdifferential of Plastria, the infradifferential of Gutiérrez, the subdifferentials of Martínez-Legaz-Sach, Penot-Volle, Thach. We complete this list by some new proposals. We compare these specific subdifferentials to some all-purpose subdifferentials used in nonsmooth analysis. We give some hints about their uses. We also point out links with duality theories.

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  1. Départment of Mathematics, Université de Pau, Avenue de l’université, 64000, Pau, France

    Jean-Paul Penot

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  1. Université Blaise Pascal, Clermont-Ferrand, France

    Jean-Pierre Crouzeix

  2. Universitat Autònoma de Barcelona, Barcelona, Spain

    Juan-Enrique Martinez-Legaz

  3. Université d’Avignon, Avignon, France

    Michel Volle

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Penot, JP. (1998). Are Generalized Derivatives Sseful for Generalized Convex Functions?. In: Crouzeix, JP., Martinez-Legaz, JE., Volle, M. (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3341-8_1

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