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Sublinear circuits for polyhedral sets

  • Sublinear circuits are generalizations of the affine circuits in matroid theory, and they arise as the convex-combinatorial core underlying constrained non-negativity certificates of exponential sums and of polynomials based on the arithmetic-geometric inequality. Here, we study the polyhedral combinatorics of sublinear circuits for polyhedral constraint sets. We give results on the relation between the sublinear circuits and their supports and provide necessary as well as sufficient criteria for sublinear circuits. Based on these characterizations, we provide some explicit results and enumerations for two prominent polyhedral cases, namely the non-negative orthant and the cube [− 1,1]n.
Metadaten
Verfasserangaben:Helen Naumann, Thorsten TheobaldORCiDGND
URN:urn:nbn:de:hebis:30:3-640534
DOI:https://doi.org/10.1007/s10013-021-00528-1
ISSN:2305-2228
Titel des übergeordneten Werkes (Englisch):Vietnam journal of mathematics
Verlag:Springer
Verlagsort:Singapore
Dokumentart:Wissenschaftlicher Artikel
Sprache:Englisch
Datum der Veröffentlichung (online):06.10.2021
Datum der Erstveröffentlichung:06.10.2021
Veröffentlichende Institution:Universitätsbibliothek Johann Christian Senckenberg
Datum der Freischaltung:09.02.2022
Freies Schlagwort / Tag:Non-negativity certificate; Polyhedron; Positive function; Sublinear circuit; Sums of arithmetic-geometric exponentials
Jahrgang:2021
Seitenzahl:22
Bemerkung:
Open Access funding enabled and organized by Projekt DEAL.
HeBIS-PPN:492134030
Institute:Informatik und Mathematik
DDC-Klassifikation:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Klassifikation:05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Bxx Designs and configurations (For applications of design theory, see 94C30) / 05B35 Matroids, geometric lattices [See also 52B40, 90C27]
14-XX ALGEBRAIC GEOMETRY / 14Pxx Real algebraic and real analytic geometry / 14P05 Real algebraic sets [See also 12Dxx]
52-XX CONVEX AND DISCRETE GEOMETRY / 52Axx General convexity / 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming
Sammlungen:Universitätspublikationen
Lizenz (Deutsch):License LogoCreative Commons - Namensnennung 4.0

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