Linear Programming: A Modern Integrated Analysis
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer US
1995
|
| Edition: | 1st ed. 1995 |
| Series: | International Series in Operations Research & Management Science
1 |
| Subjects: | |
| Online Access: | BTU01 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (XIII, 342 p) |
| ISBN: | 9781461523116 |
| DOI: | 10.1007/978-1-4615-2311-6 |
Staff View
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| 520 | |a 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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| spelling | Saigal, Romesh Verfasser aut Linear Programming A Modern Integrated Analysis by Romesh Saigal 1st ed. 1995 New York, NY Springer US 1995 1 Online-Ressource (XIII, 342 p) txt rdacontent c rdamedia cr rdacarrier International Series in Operations Research & Management Science 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 Operations Research/Decision Theory Mathematical Modeling and Industrial Mathematics Optimization Calculus of Variations and Optimal Control; Optimization Operations research Decision making Mathematical models Mathematical optimization Calculus of variations Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-604 Erscheint auch als Druck-Ausgabe 9781461359777 Erscheint auch als Druck-Ausgabe 9780792396222 Erscheint auch als Druck-Ausgabe 9781461523123 https://doi.org/10.1007/978-1-4615-2311-6 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Saigal, Romesh Linear Programming A Modern Integrated Analysis Operations Research/Decision Theory Mathematical Modeling and Industrial Mathematics Optimization Calculus of Variations and Optimal Control; Optimization Operations research Decision making Mathematical models Mathematical optimization Calculus of variations Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | Linear Programming A Modern Integrated Analysis |
| title_auth | Linear Programming A Modern Integrated Analysis |
| title_exact_search | Linear Programming A Modern Integrated Analysis |
| title_exact_search_txtP | Linear Programming A Modern Integrated Analysis |
| title_full | Linear Programming A Modern Integrated Analysis by Romesh Saigal |
| title_fullStr | Linear Programming A Modern Integrated Analysis by Romesh Saigal |
| title_full_unstemmed | Linear Programming A Modern Integrated Analysis by Romesh Saigal |
| title_short | Linear Programming |
| title_sort | linear programming a modern integrated analysis |
| title_sub | A Modern Integrated Analysis |
| topic | Operations Research/Decision Theory Mathematical Modeling and Industrial Mathematics Optimization Calculus of Variations and Optimal Control; Optimization Operations research Decision making Mathematical models Mathematical optimization Calculus of variations Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Operations Research/Decision Theory Mathematical Modeling and Industrial Mathematics Optimization Calculus of Variations and Optimal Control; Optimization Operations research Decision making Mathematical models Mathematical optimization Calculus of variations Lineare Optimierung |
| url | https://doi.org/10.1007/978-1-4615-2311-6 |
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