Various Lipschitz-Like Properties for Functions and Sets. II: Subdifferential and Normal Characterizations

Rafael Correa; Pedro Gajardo; Lionel Thibault

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

K-directionally Lipschitzian function
epi-Lipschitzian set
compactly epi-Lipschitzian set
subdifferential
normal cone
multidirectional mean value inequality

Mathematics Subject Classification

26A24, 49J52; 28B20, 47L07

Suggested citation

R. Correa, P. Gajardo, L. Thibault. “Various Lipschitz-Like Properties for Functions and Sets. II: Subdifferential and Normal Characterizations.” Journal of Convex Analysis 27 (2020), No. 1, 237–276.