Convex composite functions in Banach spaces and the primal lower-nice property
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- by C. Combari, A. Elhilali Alaoui, A. Levy, R. Poliquin and L. Thibault PDF
- Proc. Amer. Math. Soc. 126 (1998), 3701-3708 Request permission
Abstract:
Primal lower-nice functions defined on Hilbert spaces provide examples of functions that are “integrable” (i.e. of functions that are determined up to an additive constant by their subgradients). The class of primal lower-nice functions contains all convex and lower-$C^2$ functions. In finite dimensions the class of primal lower-nice functions also contains the composition of a convex function with a $C^2$ mapping under a constraint qualification. In Banach spaces certain convex composite functions were known to be primal lower-nice (e.g. a convex function had to be continuous relative to its domain). In this paper we weaken the assumptions and provide new examples of convex composite functions defined on a Banach space with the primal lower-nice property. One consequence of our results is the identification of new examples of integrable functions on Hilbert spaces.References
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Additional Information
- C. Combari
- Affiliation: Université de Montpellier II, Laboratoire Analyse Convexe, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France
- A. Elhilali Alaoui
- Affiliation: Université de Montpellier II, Laboratoire Analyse Convexe, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France
- Address at time of publication: Falculté des Sciences et Techniques de Marrakech, Université Cadi Ayad, B.P. 618, Marrakech, Maroc
- A. Levy
- Affiliation: Department of Mathematics, Bowdoin College, Brunswick, Maine 04011
- Email: alevy@bowdoin.edu
- R. Poliquin
- Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- Email: rene.poliquin@ualberta.ca
- L. Thibault
- Affiliation: Université de Montpellier II, Laboratoire Analyse Convexe, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France
- Received by editor(s): February 16, 1996
- Received by editor(s) in revised form: November 27, 1996
- Additional Notes: The research of R. Poliquin was supported in part by the Natural Sciences and Engineering Research Council of Canada under grant OGP41983.
- Communicated by: Dale Alspach
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3701-3708
- MSC (1991): Primary 58C20; Secondary 49J52
- DOI: https://doi.org/10.1090/S0002-9939-98-04324-X
- MathSciNet review: 1451793