On the expected condition number of linear programming problems
type: Item
instance of: scholarly article
title: On the expected condition number of linear programming problems
zbMATH Open document ID: 1030.65039
author: Felipe Cucker
author: Mario Wschebor
published in: Numerische Mathematik
publication date: 2003-08-19T00:00:00Z
review text: The authors examine the condition number \(C(A)\) introduced by \textit{D. Cheung} and \textit{F. Cucker} [Math. Program. 91A, No. 1, 163-174 (2001; Zbl 1072.90564)] for linear programming. It is assumed that the matrix coefficients are independent, identically distributed standard Gaussian random variables. The moments of \(C(A)\) are estimated. When \(n\) is sufficiently larger than \(m\), when \(A\) is \(m\times n\), then \(E(\ln(C(A))= \max\{\ln m,\ln\ln n\}+ O(1)\). Bounds of an alternative condition number are also estimated.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 1967707
zbMATH Keywords: condition number
zbMATH Keywords: linear programming
reviewed by: F. Szidarovszky
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: s00211-002-0385-1
OpenAlex ID: W2049154861
Wikidata QID: Q57733248
DBLP publication ID: journals/nm/CuckerW03
DOI: 10.1007/S00211-002-0385-1
description: scientific article; zbMATH DE number 1967707