V. G. Naidenko, “Partial Convexity”, Mat. Zametki, 75:2 (2004), 222–235; Math. Notes, 75:2 (2004), 202

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Matematicheskie Zametki, 2004, Volume 75, Issue 2, Pages 222–235
DOI: https://doi.org/10.4213/mzm29 (Mi mzm29)

This article is cited in 5 scientific papers (total in 5 papers)

Partial Convexity

V. G. Naidenko

Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

Full-text PDF (234 kB) Citations (5)

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DOI: https://doi.org/10.4213/mzm29

Abstract: We study

O C

$OC$ -convexity, which is defined by the intersection of conic semispaces of partial convexity. We investigate an optimization problem for

O C

$OC$ -convex sets and prove a Krein–Milman type theorem for

O C

$OC$ -convexity. The relationship between

O C

$OC$ -convex and functionally convex sets is studied. Topological and numerical aspects, as well as separability properties are described. An upper estimate for the Carathéodory number for

O C

$OC$ -convexity is found. On the other hand, it happens that the Helly and the Radon number for

O C

$OC$ -convexity are infinite. We prove that the

O C

$OC$ -convex hull of any finite set of points is the union of finitely many polyhedra.

Received: 12.07.2002

English version:
Mathematical Notes, 2004, Volume 75, Issue 2, Pages 202–212
DOI: https://doi.org/10.1023/B:MATN.0000015036.94515.c0

Bibliographic databases:

UDC: 514+681.3

Language: Russian

Citation: V. G. Naidenko, “Partial Convexity”, Mat. Zametki, 75:2 (2004), 222–235; Math. Notes, 75:2 (2004), 202–212

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm29

https://doi.org/10.4213/mzm29

https://www.mathnet.ru/eng/mzm/v75/i2/p222

This publication is cited in the following 5 articles:

David Flores-Peñaloza, Mario A. Lopez, Nestaly Marín, David Orden, “An efficient algorithm for identifying rainbow ortho-convex 4-sets in k-colored point sets”, Information Processing Letters, 189 (2025), 106551
V. G. Naidenko, “Topology of directional convexity”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 56:4 (2020), 408
A. M. Dulliev, “Properties of Connected Ortho-convex Sets in the Plane”, Math. Notes, 101:3 (2017), 443–459
A. M. Dulliev, “Two Structures Based on Convexities on the 2-Sphere”, Math. Notes, 102:2 (2017), 156–163
V. G. Naidenko, “Contractibility of Half-Spaces of Partial Convexity”, Math. Notes, 85:6 (2009), 868–876

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	195
References:	38
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