<div class="csl-bib-body">
<div class="csl-entry">Daniilidis, A., De Bernardi, C. A., & Miglierina, E. (2024). <i>ABB Theorems: results and limitations in infinite dimensions</i>. arXiv. https://doi.org/10.48550/arXiv.2407.10509</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/204024
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dc.description.abstract
We construct a weakly compact convex subset of ℓ2 with nonempty interior that has an isolated maximal element, with respect to the lattice order ℓ2+. Moreover, the maximal point cannot be supported by any strictly positive functional, showing that the Arrow-Barankin-Blackwell theorem fails. This example discloses the pertinence of the assumption that the cone has a bounded base for the validity of the result in infinite dimensions. Under this latter assumption, the equivalence of the notions of strict maximality and maximality is established
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
ABB theorem
en
dc.subject
efficient point
en
dc.subject
positive functional
en
dc.subject
density
en
dc.title
ABB Theorems: results and limitations in infinite dimensions
en
dc.type
Preprint
en
dc.type
Preprint
de
dc.identifier.arxiv
2407.10509
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dc.contributor.affiliation
Università Cattolica del Sacro Cuore, Italy
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dc.contributor.affiliation
Università Cattolica del Sacro Cuore, Italy
-
dc.relation.grantno
P 36344N
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tuw.project.title
Unilateralität und Asymmetrie in der Variationsanalyse
-
tuw.researchTopic.id
C4
-
tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
-
tuw.publication.orgunit
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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tuw.publisher.doi
10.48550/arXiv.2407.10509
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dc.description.numberOfPages
12
-
tuw.author.orcid
0000-0003-4837-694X
-
tuw.author.orcid
0000-0002-9654-1324
-
tuw.author.orcid
0000-0003-3493-8198
-
dc.description.sponsorshipexternal
INdAM
-
dc.description.sponsorshipexternal
CUP
-
dc.description.sponsorshipexternal
MICINN
-
dc.relation.grantnoexternal
GNAMPA, Professore Visitatore
-
dc.relation.grantnoexternal
E53C23001670001
-
dc.relation.grantnoexternal
PID2020-112491GB-I00
-
tuw.publisher.server
arXiv
-
wb.sciencebranch
Mathematik
-
wb.sciencebranch.oefos
1010
-
wb.sciencebranch.value
100
-
item.languageiso639-1
en
-
item.openairetype
preprint
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item.grantfulltext
none
-
item.fulltext
no Fulltext
-
item.cerifentitytype
Publications
-
item.openairecristype
http://purl.org/coar/resource_type/c_816b
-
crisitem.author.dept
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
-
crisitem.author.dept
Università Cattolica del Sacro Cuore
-
crisitem.author.dept
Università Cattolica del Sacro Cuore
-
crisitem.author.orcid
0000-0003-4837-694X
-
crisitem.author.orcid
0000-0002-9654-1324
-
crisitem.author.orcid
0000-0003-3493-8198
-
crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik
