Geodesic
Various Lipschitz-Like Properties for Functions and Sets. II: Subdifferential and Normal Characterizations
Journal of convex analysis, Tome 27 (2020) no. 1, pp. 237-276
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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.
Classification : 26A24, 49J52, 28B20, 47L07
Mots-clés : K-directionally Lipschitzian function, epi-Lipschitzian set, compactly epi-Lipschitzian set, subdifferential, normal cone, multidirectional mean value inequality 
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     author = {R. Correa and P. Gajardo and L. Thibault},
     title = {Various {Lipschitz-Like} {Properties} for {Functions} and {Sets.} {II:} {Subdifferential} and {Normal} {Characterizations}},
     journal = {Journal of convex analysis},
     pages = {237--276},
     year = {2020},
     volume = {27},
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R. Correa; P. Gajardo; L. Thibault. Various Lipschitz-Like Properties for Functions and Sets. II: Subdifferential and Normal Characterizations. Journal of convex analysis, Tome 27 (2020) no. 1, pp. 237-276. http://geodesic.mathdoc.fr/item/JCA_2020_27_1_JCA_2020_27_1_a14/