Daniilidis, A., De Bernardi, C. A., & Miglierina, E. (2024). ABB Theorems: results and limitations in infinite dimensions. arXiv. https://doi.org/10.48550/arXiv.2407.10509
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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ArXiv ID:
2407.10509
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Date (published):
15-Jul-2024
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Number of Pages:
12
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Preprint Server:
arXiv
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Keywords:
ABB theorem; efficient point; positive functional; density
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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
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Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF - Österr. Wissenschaftsfonds)
