Linear Programming : A Modern Integrated Analysis
Language: English
Published by Springer Us Nov 1995, 1995
Series: Book 4 of 323 - International Series in Operations Research & Management Science
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
US$ 375.91
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Add to basketItem description from seller
Neuware - 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.…
Seller Inventory # 9780792396222
- Title
- Linear Programming : A Modern Integrated Analysis
- Author
- Romesh Saigal
- Publisher
- Springer Us Nov 1995
- Publication year
- 1995
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 0792396227
- ISBN 13
- 9780792396222
- Item weight
- 680 grams
- Dimensions
- 234x156x21 mm
- Series
- Book 4 of 323: International Series in Operations Research & Management Science
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.
"Synopsis" may belong to another edition of this title.
Review
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)
"About the title" may belong to another edition of this title.
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