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Mat. Zametki, 2004, Volume 75, Issue 2, Pages 222–235 (Mi mz29)  

This article is cited in 3 scientific papers (total in 3 papers)

Partial Convexity

V. G. Naidenko

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

Abstract: We study $OC$-convexity, which is defined by the intersection of conic semispaces of partial convexity. We investigate an optimization problem for $OC$-convex sets and prove a Krein–Milman type theorem for $OC$-convexity. The relationship between $OC$-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 $OC$-convexity is found. On the other hand, it happens that the Helly and the Radon number for $OC$-convexity are infinite. We prove that the $OC$-convex hull of any finite set of points is the union of finitely many polyhedra.

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

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English version:
Mathematical Notes, 2004, 75:2, 202–212

Bibliographic databases:

UDC: 514+681.3
Received: 12.07.2002

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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\pages 202--212
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. G. Naidenko, “Contractibility of Half-Spaces of Partial Convexity”, Math. Notes, 85:6 (2009), 868–876  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. M. Dulliev, “Properties of Connected Ortho-convex Sets in the Plane”, Math. Notes, 101:3 (2017), 443–459  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. M. Dulliev, “Two Structures Based on Convexities on the 2-Sphere”, Math. Notes, 102:2 (2017), 156–163  mathnet  crossref  crossref  mathscinet  isi  elib
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