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Linear programming. / v. 2, Theory and Extensions

Author: George Bernard Dantzig; Mukund Narain Thapa
Publisher: New York : Springer, 2003.
Series: Springer series in operations research.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:

Linear programming represents one of the major applications of mathematics to business, industry, and economics. This second volume includes advanced topics including variants of the simplex method,  Read more...

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Additional Physical Format: Print version:
Dantzig, George Bernard, 1914-
Linear programming. v. 2, Theory and Extensions.
New York : Springer, 2003
(DLC) 96036411
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: George Bernard Dantzig; Mukund Narain Thapa
ISBN: 9780387215693 0387215697 0387215697
OCLC Number: 424377983
Notes: Titre de l'écran-titre (visionné le 20 mai 2008).
Description: 1 online resource.
Contents: Cover --
About the authors --
Table of contents --
List of figures --
List of tables --
Preface --
Definition of symbols --
Chapter 1 Geometry of linear inequality systems and the simplex method --
1.1 Convexity and linear inequality systems --
1.2 Simplex defined --
1.3 Global minimum, extreme points, and edges --
1.4 The simplex method viewed as the steepest descent along edges --
1.5 The simplex interpretation of the simplex method --
1.6 Notes & selected bibliography --
1.7 Problems --
Chapter 2 Duality and theorems of the alternatives --
2.1 The duality theorem --
2.2 Additional theorems on duality --
2.3 Complementary slackness --
2.4 Theorems of the alternatives --
2.5 Notes & selected bibliography --
2.6 Problems --
Chapter 3 Early interior-point methods --
3.1 Von Neumann's method --
3.2 Dikin's method --
3.3 Karmarkar's method --
3.4 Notes & selected bibliography --
3.5 Problems --
Chapter 4 Interior-point methods --
4.1 Newton's method --
4.2 The linear least-squares problem --
4.3 Barrier function methods --
4.4 The primal logarithmic barrier method for solving linear programs --
4.5 Primal-dual logarithmic barrier methods --
4.6 Recovering a basic feasible solution --
4.7 Computational comments --
4.8 Notes & selected bibliography --
4.9 Problems --
Chapter 5 Degeneracy --
5.1 Examples of cycling --
5.2 On resolving degeneracy --
5.3 Dantzig's inductive method --
5.4 Wolfe's rule --
5.5 Bland's rule --
5.6 Krishna's extra column rule --
5.7 On avoiding degenerate pivots --
5.8 Notes & selected bibliography --
5.9 Problems --
Chapter 6 Variants of the simplex method --
6.1 Introduction --
6.2 Max improvement per iteration --
6.3 Dual-simplex method --
6.4 Parametric linear programs --
6.5 Self-dual parametric algorithm --
6.6 The primal-dual algorithm --
6.7 The phase I least-squares algorithm --
6.8 Notes & selected bibliography --
6.9 Problems --
Chapter 7 Transportation problem and variations --
7.1 The classical transportation problem --
7.2 Finding an initial solution --
7.3 Finding an improved basic solution --
7.4 Degeneracy in the transportation problem --
7.5 Transshipment problem --
7.6 Transportation problems with bounded partial sums --
7.7 Notes & selected bibliography --
7.8 Problems --
Chapter 8 Network flow theory --
8.1 The maximal flow problem --
8.2 Shortest route --
8.3 Minimum cost-flow problem --
8.4 Notes & selected bibliography --
8.5 Problems --
Chapter 9 Generalized upper bounds --
9.1 Problem statement --
9.2 Basic theory --
9.3 Solving systems with GUB equations --
9.4 Updating the basis and working basis --
9.5 Notes & selected bibliography --
9.6 Problems --
Chapter 10 Decomposition of large-scale systems --
10.1 Wolfe's generalized linear program --
10.2 Dantzig-Wolfe (d-w) decomposition principle --
10.3 Benders decomposition --
10.4 Block-angular system --
10.5 Staircase structured problems --
10.6 Decomposition used in central planning --
10.7 Notes & selected bibliography --
10.8 Problems --
chapter 11 Sto.
Series Title: Springer series in operations research.
Responsibility: George B. Dantzig, Mukund N. Thapa.
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