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.
Author:Helen Naumann, Thorsten Theobald
Parent Title (English):Vietnam journal of mathematics
Place of publication:Singapore
Document Type:Article
Date of Publication (online):2021/10/06
Date of first Publication:2021/10/06
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/02/09
Tag:Non-negativity certificate; Polyhedron; Positive function; Sublinear circuit; Sums of arithmetic-geometric exponentials
Page Number:22
Open Access funding enabled and organized by Projekt DEAL.
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification: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
Licence (German):License LogoCreative Commons - Namensnennung 4.0