Linear and Integer Programming vs Linear Integration and Counting
A Duality Viewpoint
Seiten
2010
|
Softcover reprint of hardcover 1st ed. 2009
Springer-Verlag New York Inc.
978-1-4419-1853-6 (ISBN)
Springer-Verlag New York Inc.
978-1-4419-1853-6 (ISBN)
This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (or counting). The book provides some new insights on duality concepts for integer programs.
Integer programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely ef?cient LP software packages exist, solving an integer program can remain a formidable challenge, even for some small size problems. For instance, the following small (5-variable) IP problem (called the unbounded knapsack problem) min{213x?1928x?11111x?2345x +9123x} 1 2 3 4 5 s.t. 12223x +12224x +36674x +61119x +85569x = 89643482, 1 2 3 4 5 x ,x ,x ,x ,x?N, 1 2 3 4 5 taken from a list of dif?cult knapsack problems in Aardal and Lenstra [2], is not solved even by hours of computing, using for instance the last version of the ef?cient software package CPLEX. However,thisisnotabookonintegerprogramming,asverygoodonesonthistopicalreadyexist. For standard references on the theory and practice of integer programming, the interested reader is referred to, e.g., Nemhauser and Wolsey [113], Schrijver [121], Wolsey [136], and the more recent Bertsimas and Weismantel [21]. On the other hand, this book could provide a complement to the above books as it develops a rather unusual viewpoint.
Integer programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely ef?cient LP software packages exist, solving an integer program can remain a formidable challenge, even for some small size problems. For instance, the following small (5-variable) IP problem (called the unbounded knapsack problem) min{213x?1928x?11111x?2345x +9123x} 1 2 3 4 5 s.t. 12223x +12224x +36674x +61119x +85569x = 89643482, 1 2 3 4 5 x ,x ,x ,x ,x?N, 1 2 3 4 5 taken from a list of dif?cult knapsack problems in Aardal and Lenstra [2], is not solved even by hours of computing, using for instance the last version of the ef?cient software package CPLEX. However,thisisnotabookonintegerprogramming,asverygoodonesonthistopicalreadyexist. For standard references on the theory and practice of integer programming, the interested reader is referred to, e.g., Nemhauser and Wolsey [113], Schrijver [121], Wolsey [136], and the more recent Bertsimas and Weismantel [21]. On the other hand, this book could provide a complement to the above books as it develops a rather unusual viewpoint.
I Linear Integration and Linear Programming.- The Linear Integration Problem I.- Comparing the Continuous Problems P and I.- II Linear Counting and Integer Programming.- The Linear Counting Problem I.- Relating the Discrete Problems P and I with P.- III Duality.- Duality and Gomory Relaxations.- Barvinok#x2019;s Counting Algorithm and Gomory Relaxations.- A Discrete Farkas Lemma.- The Integer Hull of a Convex Rational Polytope.- Duality and Superadditive Functions.
| Reihe/Serie | Springer Series in Operations Research and Financial Engineering |
|---|---|
| Zusatzinfo | 2 Illustrations, black and white; XIV, 168 p. 2 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 178 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Wirtschaft ► Betriebswirtschaft / Management | |
| Schlagworte | Brion • interger programming • linear integration • Linear Programming • linear summation • Vergne |
| ISBN-10 | 1-4419-1853-1 / 1441918531 |
| ISBN-13 | 978-1-4419-1853-6 / 9781441918536 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
was jeder über Informatik wissen sollte
Buch | Softcover (2024)
Springer Vieweg (Verlag)
CHF 53,15
Grundlagen – Anwendungen – Perspektiven
Buch | Softcover (2022)
Springer Vieweg (Verlag)
CHF 48,95
Eine Einführung in die Systemtheorie
Buch | Softcover (2022)
UTB (Verlag)
CHF 34,95
