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Continuous Fréchet Differentiability of the Moreau Envelope of Convex Functions on Banach Spaces.
- Source :
- Journal of Optimization Theory & Applications; Dec2022, Vol. 195 Issue 3, p1007-1018, 12p
- Publication Year :
- 2022
-
Abstract
- It is shown that the Moreau envelope of a convex lower semicontinuous function on a real Banach space with strictly convex dual is Fréchet differentiable at every its minimizer, and continuously Fréchet differentiable at every its non-minimizer satisfying that the dual space is uniformly convex at every norm one element around its normalized gradient vector at those points. As an application, we obtain the continuous Fréchet differentiability of the Moreau envelope functions on Banach spaces with locally uniformly duals and the continuity of the corresponding proximal mappings provided that both primal and dual spaces are locally uniformly convex. [ABSTRACT FROM AUTHOR]
- Subjects :
- BANACH spaces
FUNCTION spaces
CONVEX functions
DIFFERENTIABLE functions
Subjects
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 195
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 160256350
- Full Text :
- https://doi.org/10.1007/s10957-022-02126-8