<div class="csl-bib-body">
<div class="csl-entry">Daniilidis, A. (2022, August 9). <i>Determining a function via the modulus of its derivative</i> [Presentation]. Modern Nonsmooth Optimization - A Workshop in honor of the 60th Birthday of Adrian Lewis, University of Washington, Seattle, United States of America (the).</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/152403
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dc.description
A workshop in honour of the 60th Birthday of Adrian Lewis
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dc.description.abstract
Let H be a Hilbert space and f; g : H ! R be two C2-smooth convex and
bounded from below functions. In this setting one has:
krfk = krgk if and only if rf = rg:
In other words, every smooth convex and bounded from below function is
determined (up to a constant) by the modulus of its derivative. The above
result has been extended to nonsmooth (convex bounded from below) func-
tions, using the remoteness of the subdiferential (i.e. its distance to zero),
notion which coincides with the metric slope. In this talk we show that,
surprisingly enough, the above results do not fundamentally rely neither on
convexity nor on the linear structure of the ambient space. A consequence
of our main result is that every Lipschitz, inf-compact function in a metric
space is uniquely determined by its slope and its (metric) critical values.
If time allows, we shall discuss further extensions to more abstract settings.
1
en
dc.language.iso
en
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dc.subject
Hibert Space
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dc.subject
Metric slope
en
dc.subject
Nonsmooth
en
dc.subject
Lipschitz
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dc.title
Determining a function via the modulus of its derivative
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik
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tuw.author.orcid
0000-0003-4837-694X
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tuw.event.name
Modern Nonsmooth Optimization - A Workshop in honor of the 60th Birthday of Adrian Lewis
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tuw.event.startdate
09-08-2022
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tuw.event.enddate
10-08-2022
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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
University of Washington, Seattle
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tuw.event.country
US
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tuw.event.institution
Pacific Institute of Mathematical Sciences
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tuw.event.presenter
Daniilidis, Aris
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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 presentation
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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/R60J-J5BD
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crisitem.author.dept
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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crisitem.author.orcid
0000-0003-4837-694X
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crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik