Linear Programming - A Modern Integrated Analysis (Hardcover, 1995 ed.)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	International Series in Operations Research & Management Science, 1
Release date:	November 1995
First published:	1995
Authors:	Romesh Saigal
Dimensions:	235 x 155 x 20mm (L x W x T)
Format:	Hardcover
Pages:	342
Edition:	1995 ed.
ISBN-13:	978-0-7923-9622-2
Categories:	Books > Business & Economics > Business & management > Management & management techniques > Operational research Books > Science & Mathematics > Mathematics > Optimization > Linear programming Promotions
LSN:	0-7923-9622-7
Barcode:	9780792396222

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