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Other titles in the International Series in Operations Research & Management Science series:

International Series in Operations Research & Management Science #1: Linear Programming: A Modern Integrated Analysis

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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.

Table of Contents

Preface. 1. Introduction. 2. Background. 3. Duality theory and optimality conditions. 4. Boundary methods. 5. Interior point methods. 6. Implementation. A: Tables. Bibliography. Index.

Product Details

ISBN:
9781461359777
Author:
Saigal, Romesh
Publisher:
Springer
Location:
Boston, MA
Subject:
Operations Research
Subject:
Operation Research/Decision Theory
Subject:
Mathematical Modeling and Industrial Mathematics
Subject:
OPTIMIZATION
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
Mathematics-Computer
Subject:
Economics
Subject:
Language, literature and biography
Subject:
Operations Research/Decision Theory
Subject:
Business and Economics
Subject:
Mathematical optimization
Copyright:
Edition Description:
Softcover reprint of the original 1st ed. 1995
Series:
International Series in Operations Research & Management Science
Series Volume:
1
Publication Date:
20121231
Binding:
TRADE PAPER
Language:
English
Pages:
355
Dimensions:
235 x 155 mm

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International Series in Operations Research & Management Science #1: Linear Programming: A Modern Integrated Analysis New Trade Paper
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Product details 355 pages Springer - English 9781461359777 Reviews:
"Synopsis" by , 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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