Linear Programming: A Modern Integrated Analysis: 1 (International Series in Operations Research & Management Science) - Tapa blanda

Libro 4 de 323: International Series in Operations Research & Management Science

Saigal, Romesh

 
9781461359777: Linear Programming: A Modern Integrated Analysis: 1 (International Series in Operations Research & Management Science)
Tapa blanda
ISBN 10: 1461359775 ISBN 13: 9781461359777
Editorial: Springer, 2012

Sinopsis

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.

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Críticas

`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)

Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2012
Idioma
Inglés
ISBN 10 
1461359775
ISBN 13 
9781461359777
Encuadernación
Tapa blanda
Número de páginas
360
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9780792396222: Linear Programming: A Modern Integrated Analysis: 1 (International Series in Operations Research & Management Science, 1)

Edición Destacada

ISBN 10:  0792396227 ISBN 13:  9780792396222
Editorial: Springer, 1995
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