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Auteur principal: Gorokhovik, Valentin V.
Format: Preprint
Publié: 2025
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Accès en ligne:https://arxiv.org/abs/2506.08742
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author Gorokhovik, Valentin V.
author_facet Gorokhovik, Valentin V.
contents In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the terms of generalized semispaces, the second -- in the terms of compatible complete (total) preorders, and the third -- in the terms of step-affine functions. All three characterization are equivalent each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in finite-dimensional settings by Martinez-Legaz J.-E. (Acta Mathematica Vietnamica. 1997. Vol. 22, No.~1, P. 207--211).
format Preprint
id arxiv_https___arxiv_org_abs_2506_08742
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces
Gorokhovik, Valentin V.
Optimization and Control
52A05, 52A99
In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the terms of generalized semispaces, the second -- in the terms of compatible complete (total) preorders, and the third -- in the terms of step-affine functions. All three characterization are equivalent each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in finite-dimensional settings by Martinez-Legaz J.-E. (Acta Mathematica Vietnamica. 1997. Vol. 22, No.~1, P. 207--211).
title Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces
topic Optimization and Control
52A05, 52A99
url https://arxiv.org/abs/2506.08742