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＜電子ブック＞
Linear Optimization Problems with Inexact Data / by Miroslav Fiedler, Josef Nedoma, Jaroslav Ramik, Jiri Rohn, Karel Zimmermann

版	1st ed. 2006.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XVI, 214 p. 5 illus : online resource
著者標目	*Fiedler, Miroslav author Nedoma, Josef author Ramik, Jaroslav author Rohn, Jiri author Zimmermann, Karel author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Algebras, Linear LCSH:Game theory LCSH:Operations research LCSH:Management science FREE:Optimization FREE:Linear Algebra FREE:Game Theory FREE:Operations Research, Management Science
一般注記	Matrices -- Solvability of systems of interval linear equations and inequalities -- Interval linear programming -- Linear programming with set coefficients -- Fuzzy linear optimization -- Interval linear systems and optimization problems over max-algebras Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework. Audience This book is intended for postgraduate or graduate students in the areas of operations research, optimization theory, linear algebra, interval analysis, reliable computing, and fuzzy sets. The book will also be useful for researchers in these respective areas HTTP:URL=https://doi.org/10.1007/0-387-32698-7

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