Max-plus algebra and mathematical fear in dynamic optimization
type: Item
instance of: scholarly article
title: Max-plus algebra and mathematical fear in dynamic optimization
zbMATH Open document ID: 0963.93055
DOI: 10.1023/A:1008718323759
author: Pierre Bernhard
published in: Set-Valued Analysis
publication date: 2001-03-22T00:00:00Z
review text: The reviewed paper is devoted to the max-plus algebra, a special case of Maslov's idempotent algebras, consisting of the set \(\overline R = R \cup \{ -\infty \}\) endowed with the operations \(\max\) and \(+\). Basic notions of the max-plus algebra and the corresponding linear algebra are presented. Its applications for solving a production scheduling problem as well as for discrete dynamic programming are illustrated. Interrelations between cost and probability measures are shown and the notion of Mathematical Fear -- an analogue of expectation -- are introduced and analyzed. Some applications for design and control in the imperfect information case are outlined.
Mathematics Subject Classification ID: 93C65
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 90B30
Mathematics Subject Classification ID: 90C39
zbMATH DE Number: 1523576
zbMATH Keywords: max-plus algebra
zbMATH Keywords: cost measures
zbMATH Keywords: mathematical fear
zbMATH Keywords: control in imperfect information
zbMATH Keywords: production scheduling
zbMATH Keywords: discrete dynamic programming
reviewed by: V. G. Skobelev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1523576