Diameter and Curvature: Intriguing Analogies

DOI10.1016/j.endm.2008.06.044zbMath1267.52021OpenAlexW2119035560MaRDI QIDQ5301011

Feng Xie, Antoine Deza, Yuriy Zinchenko, Tamás Terlaky

Publication date: 28 June 2013

Published in: Electronic Notes in Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.endm.2008.06.044

zbMATH Keywords

arrangementspolytopescontinuous \(d\)-step and hirsch conjectures

Mathematics Subject Classification ID

Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35)

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An analogue of the Klee-Walkup result for sonnevend's curvature of the central path, Comments on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes

Cites Work

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• Polytopes and arrangements: diameter and curvature
• Probabilistic analysis of optimization algorithms - some aspects from a practical point of view
• Many polytopes meeting the conjectured Hirsch bound
• More polytopes meeting the conjectured Hirsch bound
• Higher Bruhat orders and cyclic hyperplane arrangements
• On the curvature of the central path of linear programming theory
• The \(d\)-step conjecture for polyhedra of dimension \(d<6\)
• A Mathematical View of Interior-Point Methods in Convex Optimization
• Hyperplane Arrangements with Large Average Diameter
• Lectures on Polytopes
• Convex Polytopes
• Interior Point Methods for Linear Optimization
• On counting the \(k\)-face cells of cyclic arrangements