International Series in Operations Research & Management Science

Linear Programming

A Modern Integrated Analysis

Authors: Saigal, Romesh

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  • ISBN 978-1-4615-2311-6
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Hardcover $259.00
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About this book

In Linear Programming: A Modern Integrated Analysis, both boundary (simplex) and interior point methods are derived from the complementary slackness theorem and, unlike most books, the duality theorem is derived from Farkas's Lemma, which is proved as a convex separation theorem. The tedium of the simplex method is thus avoided.
A new and inductive proof of Kantorovich's Theorem is offered, related to the convergence of Newton's method. Of the boundary methods, the book presents the (revised) primal and the dual simplex methods. An extensive discussion is given of the primal, dual and primal-dual affine scaling methods. In addition, the proof of the convergence under degeneracy, a bounded variable variant, and a super-linearly convergent variant of the primal affine scaling method are covered in one chapter. Polynomial barrier or path-following homotopy methods, and the projective transformation method are also covered in the interior point chapter. Besides the popular sparse Cholesky factorization and the conjugate gradient method, new methods are presented in a separate chapter on implementation. These methods use LQ factorization and iterative techniques.

Reviews

`I recommend this book to anyone desiring a deep understanding of the simplex method, interior-point methods, and the connections between them.'
Interfaces, 27:2 (1997)
The book is clearly written. ... It is highly recommended to anybody wishing to get a clear insight in the field and in the role that duality plays not only from a theoretical point of view but also in connection with algorithms.'
Optimization, 40 (1997)

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $139.00
price for USA in USD
  • ISBN 978-1-4615-2311-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $259.00
price for USA in USD
  • ISBN 978-0-7923-9622-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $179.99
price for USA in USD
  • ISBN 978-1-4613-5977-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Linear Programming
Book Subtitle
A Modern Integrated Analysis
Authors
Series Title
International Series in Operations Research & Management Science
Series Volume
1
Copyright
1995
Publisher
Springer US
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4615-2311-6
DOI
10.1007/978-1-4615-2311-6
Hardcover ISBN
978-0-7923-9622-2
Softcover ISBN
978-1-4613-5977-7
Series ISSN
0884-8289
Edition Number
1
Number of Pages
XIII, 342
Topics