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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

Pedro Gajardo
Dep. de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile

Lionel Thibault
Institut Montpelliérain A. Grothendieck, Université de Montpellier, France

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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