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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Author:Karl-Heinz Küfer
URN (permanent link):urn:nbn:de:hbz:386-kluedo-50483
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (245)
Document Type:Report
Language of publication:English
Publication Date:2017/11/08
Year of Publication:1993
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/08
Number of page:15
Faculties / Organisational entities: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)