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A Unified Asymptotic Prohabilistic Analysis of Polyhedral Functionals

  • Let \(A\):= {\(a_i\mid i= 1,\dots,m\)} be an i.i.d. random sample in (\mathbb{R}^n\), which we consider a random polyhedron, either as the convex hull of the \(a_i\) or as the intersection of halfspaces {\(x \mid a ^T_i x\leq 1\)}. We introduce a class of polyhedral functionals we will call "additive-type functionals", which covers a number of polyhedral functionals discussed in different mathematical fields, where the emphasis in our contribution will be on those, which arise in linear optimization theory. The class of additive-type functionals is a suitable setting in order to unify and to simplify the asymptotic probabilistic analysis of first and second moments of polyhedral functionals. We provide examples of asymptotic results on expectations and on variances.

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Metadaten
Author:Karl-Heinz Küfer
URN:urn:nbn:de:hbz:386-kluedo-50483
Series (Serial Number):Preprints (rote Reihe) des Fachbereich Mathematik (245)
Document Type:Report
Language of publication:English
Date of Publication (online):2017/11/08
Year of first Publication:1993
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/08
Page Number:15
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)