<div class="csl-bib-body">
<div class="csl-entry">Daniilidis, A., De Bernardi, C. A., & Miglierina, E. (2025). ABB theorems: results and limitations in infinite dimensions. <i>Journal of Optimization Theory and Applications</i>, <i>207</i>(2), Article 38. https://doi.org/10.1007/s10957-025-02797-z</div>
</div>
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dc.identifier.issn
0022-3239
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/220500
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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 ℓ+2 . Moreover, the maximal point cannot be supported by any strictly positive functional, which shows 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.publisher
SPRINGER/PLENUM PUBLISHERS
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dc.relation.ispartof
Journal of Optimization Theory and Applications
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
ABB theorem
en
dc.subject
Density
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dc.subject
Efficient point
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dc.subject
Positive functional
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dc.title
ABB theorems: results and limitations in infinite dimensions
