Linear Programming: A Modern Integrated Analysis (International Series in Operations Research & Management Science) [Hardcover]

Romesh Saigal (Author)

Book Description

ISBN-10: 0792396227 | ISBN-13: 978-0792396222 | Publication Date: November 30, 1995 | Edition: 1

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.

Editorial Reviews

Review

`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)

Product Details

• Hardcover: 354 pages
• Publisher: Springer; 1 edition (November 30, 1995)
• Language: English
• ISBN-10: 0792396227
• ISBN-13: 978-0792396222
• Product Dimensions: 9.3 x 6.1 x 1 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,538,543 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars A good text book on mathematics foundations for LP, September 13, 1999

By A Customer

This review is from: Linear Programming: A Modern Integrated Analysis (International Series in Operations Research & Management Science) (Hardcover)

The book meets the need for a teacher/research worker in LP theory, given the modern developments after development of Karmarkar's interior point approaches. The chapter 2 gives the basic background about analysis & numerical linear algebra. It makes duality as central theme. ( It differs from earlier OR books, where duality is introduced after simplex algorithm discussed). It is interesting to note the amount of attention paid to the issue of degeneracy. This is the special aspect of the book. The author discusses the interior point methods in a very systmeatic way; giving the necessary proofs. Last chapter discusses the implementation issues. Interestingly, the book has no figures, no diagramms. May the author is against use of them. The author could have given more details about Korbx, or the solvers available ( like AMPL, public domain interior point solvers), so that the reader is made aware the concepts dealt in the book is useful even for users of LP.