<div class="csl-bib-body">
<div class="csl-entry">Tapia Garcia, S. (2023, November 23). <i>A slope generalization of Attouch theorem</i> [Conference Presentation]. 3rd Austrian Calculus of Variations Day 2023, Vienna, Austria.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191311
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dc.description
This is a joint work with Aris Daniilidis and David Salas.
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dc.description.abstract
A classical result of variational analysis, known as Attouch theorem, establishes the equivalence between epigraphical convergence of a sequence of proper convex lower semicontinuous functions and graphical convergence of the corresponding subdifferential maps up to a normalization condition which fixes the integration constant. In this work, we show that in finite dimensions and under a mild boundedness assumption, we can replace subdifferentials (sets of vectors) by slopes (scalars, corresponding to the distance of the subdifferentials to zero) and still obtain the same characterization: namely, the epigraphical convergence of functions is equivalent to the epigraphical convergence of their slopes. This surprising result goes in line with recent developments on slope determination (Boulmezaoud, Cieutat, Daniilidis, 2018), (Pérez-Aros, Salas, Vilches, 2021) and slope sensitivity (Daniilidis, Drusvyatskiy, 2023) for convex functions.
en
dc.language.iso
en
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dc.subject
Variational alalysis
en
dc.subject
convex functions
en
dc.subject
slope determination
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dc.title
A slope generalization of Attouch theorem
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Conference Presentation
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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tuw.event.name
3rd Austrian Calculus of Variations Day 2023
en
tuw.event.startdate
23-11-2023
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tuw.event.enddate
24-11-2023
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Vienna
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tuw.event.country
AT
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tuw.event.institution
TU Wien & Universität Wien
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tuw.event.presenter
Tapia Garcia, Sebastian
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dc.relation.ispreviousversionof
https://arxiv.org/abs/2311.10849
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
conference paper not in proceedings
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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crisitem.author.dept
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik
