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Theory of Linear and Integer Programming
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See moreTheory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis.
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Description
Theory of Linear and Integer Programming by Alexander Schrijver from the Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis.
This book aims to complement the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimisation are given, and the author also includes extensive historical surveys and bibliographies.
The book is intended for graduate students and researchers in operations research, mathematics, and computer science. It will also be of interest to mathematical historians.
Contents:
1. Introduction and preliminaries
2. Problems, algorithms, and complexity
3. Linear algebra and complexity
4. Theory of lattices and linear diophantine equations
5. Algorithms for linear diophantine equations
6. Diophantine approximation and basis reduction
7. Fundamental concepts and results on polyhedra, linear inequalities, and linear programming
8. The structure of polyhedra
9. Polarity, and blocking and anti-blocking polyhedra
10. Sizes and the theoretical complexity of linear inequalities and linear programming
11. The simplex method
12. Primal-dual, elimination, and relaxation methods
13. Khachiyan's method for linear programming
14. The ellipsoid method for polyhedra more generally
15. Further polynomiality results in linear programming
16. Introduction to integer linear programming
17. Estimates in integer linear programming
18. The complexity of integer linear programming
19. Totally unimodular matrices: fundamental properties and examples
20. Recognising total unimodularity
21. Further theory related to total unimodularity
22. Integral polyhedra and total dual integrality
23. Cutting planes
24. Further methods in integer linear programming
25. Historical and further notes on integer linear programming
26. References
27. Notation index
28. Author index
29. Subject index
Book Hero Magic summarised reviews for this book. While it's new and still learning, it may not be perfect - your feedback is welcome! HOW HAS THIS BEEN REVIEWED?
Theory of Linear and Integer Programming by Alexander Schrijver is praised for its exhaustive presentation of theoretical aspects in linear and integer programming, serving as an excellent complement to more practically focused texts.
Book Details
INFORMATION
ISBN: 9780471982326
Publisher: John Wiley & Sons Inc
Format: Paperback / softback
Date Published: 27 April 1998
Country: United States
Imprint: John Wiley & Sons Inc
Audience: Tertiary education, Professional and scholarly
DIMENSIONS
Spine width: 27.0mm
Width: 157.0mm
Height: 239.0mm
Weight: 709g
Pages: 484
About the Author
Professor Schrijver has held tenured positions with the Mathematisch Centrum in Amsterdam, and the University of Amsterdam. He has spent leaves of absence in Oxford and Szeged (Hungary). In 1983 he was appointed to the post of Professor of Mathematics at Tilburg University, The Netherlands, with a partial engagement at the Centrum voor Wiskunde en Informatica in Amsterdam.
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