Journal of Convex Analysis 27 (2020), No. 1, 237--276
Copyright Heldermann Verlag 2020
Various Lipschitz-Like Properties for Functions and Sets.
II: Subdifferential and Normal Characterizations
Rafael Correa
Dep. de Ingeniería Matemática, Universidad de Chile, Santiago, Chile
and: Universidad de O'Higgins, Rancagua, Chile
rcorrea@dim.uchile.cl
Pedro Gajardo
Dep. de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile
pedro.gajardo@usm.cl
Lionel Thibault
Institut Montpelliérain A. Grothendieck, Université de Montpellier, France
lionel.thibault@umontpellier.fr
The present paper is a continuation of our previous article: Various Lipschitz-like properties of functions and sets. I: Directional derivative and tangential characterizations [SIAM J. Optim. 20(4) (2010) 1766--1785]. Here we provide diverse subdifferential and normal characterizations of K-directionally Lipschitzian functions and sets for bounded sets K of a Banach space.
Keywords: K-directionally Lipschitzian function, epi-Lipschitzian set, compactly epi-Lipschitzian set, subdifferential, normal cone, multidirectional mean value inequality.
MSC: 26A24, 49J52; 28B20, 47L07.
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