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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10127167%21RIV13-GA0-11320___
rdf:type
n3:Vysledek skos:Concept
dcterms:description
We prove that a locally Lipschitz function on an open subset G of an Asplund space X, whose restrictions to %22many lines%22 are essentially smooth (i.e., almost everywhere strictly differentiable), is generically Frechet differentiable on X. In this way we obtain new proofs of known Frechet differentiability properties of approximately convex functions, Lipschitz regular functions, saddle (or biconvex) Lipschitz functions, and essentially smooth functions (in the sense of Borwein and Moors), and also some new differentiability results (e.g., for partially DC functions). We show that classes of functions S-e(g)(G) and R-e(g)(G) (defined via linear essential smoothness) are respectively larger than classes S-e(G) (of essentially smooth functions) and R-e(G) studied by Borwein and Moors, and have also nice properties. In particular, we prove that members of S-e(g)(G) are uniquely determined by their Clarke subdifferentials. We also show the inclusion S-e(G) subset of R-e(G) for Borwein-Moors classes. We prove that a locally Lipschitz function on an open subset G of an Asplund space X, whose restrictions to %22many lines%22 are essentially smooth (i.e., almost everywhere strictly differentiable), is generically Frechet differentiable on X. In this way we obtain new proofs of known Frechet differentiability properties of approximately convex functions, Lipschitz regular functions, saddle (or biconvex) Lipschitz functions, and essentially smooth functions (in the sense of Borwein and Moors), and also some new differentiability results (e.g., for partially DC functions). We show that classes of functions S-e(g)(G) and R-e(g)(G) (defined via linear essential smoothness) are respectively larger than classes S-e(G) (of essentially smooth functions) and R-e(G) studied by Borwein and Moors, and have also nice properties. In particular, we prove that members of S-e(g)(G) are uniquely determined by their Clarke subdifferentials. We also show the inclusion S-e(G) subset of R-e(G) for Borwein-Moors classes.
dcterms:title
Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines
skos:prefLabel
Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines
skos:notation
RIV/00216208:11320/12:10127167!RIV13-GA0-11320___
n3:predkladatel
n20:orjk%3A11320
n5:aktivita
n17:I n17:P n17:Z
n5:aktivity
I, P(GA201/09/0067), Z(MSM0021620839)
n5:cisloPeriodika
1
n5:dodaniDat
n6:2013
n5:domaciTvurceVysledku
n13:7357362
n5:druhVysledku
n14:J
n5:duvernostUdaju
n19:S
n5:entitaPredkladatele
n9:predkladatel
n5:idSjednocenehoVysledku
137875
n5:idVysledku
RIV/00216208:11320/12:10127167
n5:jazykVysledku
n15:eng
n5:klicovaSlova
separable reduction; essentially smooth functions; Generic Frechet differentiability
n5:klicoveSlovo
n16:separable%20reduction n16:Generic%20Frechet%20differentiability n16:essentially%20smooth%20functions
n5:kodStatuVydavatele
DE - Spolková republika Německo
n5:kontrolniKodProRIV
[9D43A5426E95]
n5:nazevZdroje
Journal of Convex Analysis
n5:obor
n8:BA
n5:pocetDomacichTvurcuVysledku
1
n5:pocetTvurcuVysledku
1
n5:projekt
n18:GA201%2F09%2F0067
n5:rokUplatneniVysledku
n6:2012
n5:svazekPeriodika
19
n5:tvurceVysledku
Zajíček, Luděk
n5:wos
000301551300002
n5:zamer
n11:MSM0021620839
s:issn
0944-6532
s:numberOfPages
26
n10:organizacniJednotka
11320