On the graph convergence of subdifferentials of convex functions

C. Combari, Lionel Thibault

Type: Article

Publication Date: 1998-01-01

Citations: 23

DOI: https://doi.org/10.1090/s0002-9939-98-04724-8

Abstract

This paper provides another proof of the Attouch Theorem relating the epigraphical limit of sequences of convex functions to the set limit of the graphs of the subdifferentials.

Locations

Proceedings of the American Mathematical Society - View - PDF

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Action	Title	Year	Authors
+	Minimizers of the limit of Mosco converging functions	2005	Dariusz Zagrodny
+	Generalized differentiation and fixed points sets behaviors with respect to Fisher convergence	2011	Michel Geoffroy Géraldine Pascaline
+	On the Strong Convergence of Subgradients of Convex Functions	2018	Dariusz Zagrodny
+ PDF Chat	Convergence of Subdifferentials of Convexly Composite Functions	1999	C. Combari R. A. Poliquin Lionel Thibault
+	Convergence of the Associated Sequence of Normal Cones of a Mosco Convergent Sequence of Sets	2012	Xi Yin Zheng Wei Zhou
+	On the Weak £ Convergence of Subdifierentials of Convex Functions	2005	Dariusz Zagrodny
+	Limiting Subdifferentials	2012	Jean‐Paul Penot
+	Convergences of subgradients of sequences of convex functions	2013	Dariusz Zagrodny
+	Elements of Differential Calculus	2012	Jean‐Paul Penot
+	Convergence of subdifferentials and normal cones in locally uniformly convex Banach space	2014	Lionel Thibault Taron Zakaryan

Works Cited by This (19)

Action	Title	Year	Authors
+	Variational Convergence for Functions and Operators	1984	Hédy Attouch
+	Topologies on Closed and Closed Convex Sets	1993	Gerald Beer
+ PDF Chat	Mosco convergence and reflexivity	1990	Gerald Beer Jonathan M. Borwein
+	Strong solutions for parabolic variational inequalities	1978	Hédy Attouch Alain Damlamian
+	On the convergence of subdifferentials of convex functions	1993	Hédy Attouch Gerald Beer
+ PDF Chat	An extension of Attouch’s theorem and its application to second-order epi-differentiation of convexly composite functions	1992	René A. Poliquin
+	The slice topology: a viable alternative to mosco convergence in nonreflexive spaces	1992	Gerald Beer
+	On the continuity of the Young-Fenchel transform	1971	Umberto Mosco
+	Integration of Subdifferentials of Lower Semicontinuous Functions on Banach Spaces	1995	Lionel Thibault Dariusz Zagrodny
+ PDF Chat	Partial extensions of Attouch’s theorem with applications to proto-derivatives of subgradient mappings	1995	Adam B. Levy R. A. Poliquin Lionel Thibault