Applied Mathematical Sciences

Linear Optimization and Approximation

An Introduction to the Theoretical Analysis and Numerical Treatment of Semi-infinite Programs

Authors: Glashoff, K., Gustafson, S.-A.

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About this book

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con­ straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi­ gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli­ cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break­ through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi­ tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-1-4612-1142-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase Institutional customers should get in touch with their account manager
Softcover $109.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Linear Optimization and Approximation
Book Subtitle
An Introduction to the Theoretical Analysis and Numerical Treatment of Semi-infinite Programs
Authors
Series Title
Applied Mathematical Sciences
Series Volume
45
Copyright
1983
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1142-6
DOI
10.1007/978-1-4612-1142-6
Softcover ISBN
978-0-387-90857-1
Series ISSN
0066-5452
Edition Number
1
Number of Pages
212
Topics