V $-Moreau envelope of nonconvex functions on smooth Banach spaces

We continue the study of the properties of the $ V $-Moreau envelope and generalized $ (f, \lambda) $-projection that we started in [<xref ref-type="bibr" rid="b5">5 ] . In this paper, we study the differentiability and the regularity of the $ V $-Moreau envelope and the Hö...

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Veröffentlicht in:AIMS mathematics Jg. 9; H. 10; S. 28589 - 28610
1. Verfasser: Bounkhel, Messaoud
Format: Journal Article
Sprache:Englisch
Veröffentlicht: AIMS Press 01.01.2024
Schlagworte:
generalized $ (f
lambda) $-projection
p $-uniformly convex banach spaces
q $-uniformly smooth banach spaces
uniformly generalized prox-regular sets
v $-moreau envelope
v $-prox-regular functions
ISSN:2473-6988, 2473-6988
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Abstract We continue the study of the properties of the $ V $-Moreau envelope and generalized $ (f, \lambda) $-projection that we started in [<xref ref-type="bibr" rid="b5">5 ] . In this paper, we study the differentiability and the regularity of the $ V $-Moreau envelope and the Hölder continuity of the generalized $ (f, \lambda) $-projection. Our results extend many existing results from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. Even on Hilbert spaces and for convex functions and sets, we derived new results.
AbstractList We continue the study of the properties of the $ V $-Moreau envelope and generalized $ (f, \lambda) $-projection that we started in [<xref ref-type="bibr" rid="b5">5 ] . In this paper, we study the differentiability and the regularity of the $ V $-Moreau envelope and the Hölder continuity of the generalized $ (f, \lambda) $-projection. Our results extend many existing results from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. Even on Hilbert spaces and for convex functions and sets, we derived new results.
Author Bounkhel, Messaoud
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Cites_doi 10.3934/math.20231513
10.1155/2015/478437
10.3390/math8112066
10.1090/S0002-9947-96-01544-9
10.1017/S0004972700038892
10.1016/j.jmaa.2004.11.007
10.1016/j.na.2010.04.077
10.1007/1-4020-4396-1
10.1016/j.jmaa.2004.03.010
10.1016/j.jmaa.2019.02.064
10.1007/b97650
10.1016/j.camwa.2007.01.029
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Snippet We continue the study of the properties of the $ V $-Moreau envelope and generalized $ (f, \lambda) $-projection that we started in [<xref ref-type="bibr"...
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StartPage 28589
SubjectTerms generalized $ (f
lambda) $-projection
p $-uniformly convex banach spaces
q $-uniformly smooth banach spaces
uniformly generalized prox-regular sets
v $-moreau envelope
v $-prox-regular functions
Title V $-Moreau envelope of nonconvex functions on smooth Banach spaces
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