Characterizations of convex approximate subdifferential calculus in Banach spaces
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- by R. Correa, A. Hantoute and A. Jourani PDF
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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.References
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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
- 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 - © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 4831-4854
- MSC (2010): Primary 49J53, 52A41, 46N10
- DOI: https://doi.org/10.1090/tran/6589
- MathSciNet review: 3456162