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Linear Optimization Problems with Inexact Data

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Linear Optimization Problems with Inexact Data Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Linear programming has attracted the interest of mathematicians since World War II when the first computers were constructed. Early attempts to apply linear programming methods practical problems failed, in part because of the inexactness of the data used to create the models. This book presents a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.

Table of Contents

Preface.- 1. Matrices (M. Fiedler).- 2. Solvability of systems of interval linear equations and inequalities (J. Rohn).- 3. Interval linear programming (J. Rohn).- 4. Linear programming with set coeffcients (J. Nedoma and J. Ramik).- 5. Fuzzy linear optimization (J. Ramik).- 6. Interval linear systems and optimization problems over max-algebras.- (K. Zimmermann).- References.- List of Symbols.- Index.

Product Details

ISBN:
9781441940940
Author:
Fiedler, Miroslav
Publisher:
Springer
Author:
Nedoma, Josef
Author:
Zimmermann, Karel
Author:
Ramik, Jaroslav
Author:
Rohn, Jiri
Location:
Boston, MA
Subject:
Linear Programming
Subject:
Systems of interval linear equations
Subject:
Systems of interval linear inequalities
Subject:
Weak and strong feasability
Subject:
Weak and strong solvability
Subject:
OPTIMIZATION
Subject:
Linear and Multilinear Algebras, Matrix Theory
Subject:
Game Theory, Economics, Social and Behav. Sciences
Subject:
Operations Research, Mathematical Programming
Subject:
Operations Research, Management Science Presents a unified approach to solving linear programming problems with inexact data
Subject:
Mathematics-Computer
Subject:
Applied
Subject:
Operations Research, Management Science
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Mathematical optimization
Subject:
matrix theory
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2006
Publication Date:
20101029
Binding:
TRADE PAPER
Language:
English
Pages:
230
Dimensions:
235 x 155 mm 358 gr

Related Subjects

Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Modeling

Linear Optimization Problems with Inexact Data New Trade Paper
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Product details 230 pages Springer - English 9781441940940 Reviews:
"Synopsis" by , Linear programming has attracted the interest of mathematicians since World War II when the first computers were constructed. Early attempts to apply linear programming methods practical problems failed, in part because of the inexactness of the data used to create the models. This book presents a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.
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