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Characterizations of convex approximate subdifferential calculus in Banach spaces


Authors: R. Correa, A. Hantoute and A. Jourani
Journal: Trans. Amer. Math. Soc. 368 (2016), 4831-4854
MSC (2010): Primary 49J53, 52A41, 46N10
DOI: https://doi.org/10.1090/tran/6589
Published electronically: November 12, 2015
MathSciNet review: 3456162
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Abstract: We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.


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Additional Information

R. Correa
Affiliation: Centro de Modelamiento Matemático (UMI 2807 CNRS), Departamento de Inginieria Matemática, Universidad de Chile, Avda Blanco Encalada 2120, Santiago, Chile
Email: rcorrea@dim.uchile.cl

A. Hantoute
Affiliation: Centro de Modelamiento Matemático (UMI 2807 CNRS), Departamento de Inginieria Matemática, Universidad de Chile, Avda Blanco Encalada 2120, Santiago, Chile
Email: ahantoute@dim.uchile.cl

A. Jourani
Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, UMR 5584 CNRS, B.P. 47870, 21078 – Dijon Cédex, France
Email: jourani@u-bourgogne.fr

DOI: https://doi.org/10.1090/tran/6589
Keywords: Convex functions, approximate subdifferential, calculus rules, approximate variational principle
Received by editor(s): May 23, 2013
Received by editor(s) in revised form: May 22, 2014
Published electronically: November 12, 2015
Additional Notes: This research was supported by Projects Fondecyt 1100019, ECOS-Conicyt CE2010-33 and Math-Amsud 13MATH-01.
The second author is the corresponding author
Article copyright: © Copyright 2015 American Mathematical Society