A search algorithm for the minimum location of an unimodal function of several variables
type: Item
instance of: scholarly article
zbMATH Open document ID: 0971.90081
author: P. E. Glotov
publication date: 2001-09-10T00:00:00Z
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 49K10
zbMATH DE Number: 1644400
zbMATH Keywords: unimodal functions of several variables
zbMATH Keywords: minimum location
zbMATH Keywords: search algorithm
MaRDI profile type: Publication
title: A search algorithm for the minimum location of an unimodal function of several variables
published in: Vestnik Moskovskogo Universiteta. Seriya 15
review text: The function \(J(u)\) is called unimodal on the interval \(U= [a, b]\) if there exist numbers \(\alpha, \beta\) \((a\leq\alpha\leq\beta\leq)\) such that: NEWLINENEWLINENEWLINE1) \(J(u)\) is a stricly monotonously decreasing function for \(a\leq u\leq \alpha\) (if \(\alpha < a)\); NEWLINENEWLINENEWLINE2) \(J(u)\) is a stricly monotonously increasing function for \(\beta \leq u \leq b\) (if \(\beta < b)\); NEWLINENEWLINENEWLINE3) \(J(u) = J_{*} = \inf_{u \in U} J(u)\) for \(\alpha \leq u \leq \beta.\) NEWLINENEWLINENEWLINEThe notion of unimodal function is generalized to the case of unimodal functions of several variables and an search algorithm for the minimum of the functions is given.
reviewed by: Sergei Georgievich Zhuravlev
description: scientific article; zbMATH DE number 1644400