ISBN: 9780387094144
ID: 9780387094144
This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (or counting). The focus is on duality and the novel approach puts integer programming in perspective with three associated problems, and permits one to define discrete analogues of well-known continuous duality concepts, and the rationale behind them. Also, the approach highlights the difference between the discrete and continuous cases. Central in the analysis are the continuous and discrete Brion and Vergnes formulae for linear integration and counting which are not very well-known in the optimization community. This approach provides some new insights on duality concepts for integer programs, and also permits to retrieve and shed new light on some well-known results. For instance, Gomory relaxations and the abstract superadditive dual of integer programs are re-interpreted in this algebraic approach.This book will serve graduate students and researchers in applied mathematics, optimization, operations research and computer science. Due to the substantial practical importance of some presented problems, researchers in other areas will also find this book useful. Linear and Integer Programming vs Linear Integration and Counting: This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (or counting). The focus is on duality and the novel approach puts integer programming in perspective with three associated problems, and permits one to define discrete analogues of well-known continuous duality concepts, and the rationale behind them. Also, the approach highlights the difference between the discrete and continuous cases. Central in the analysis are the continuous and discrete Brion and Vergnes formulae for linear integration and counting which are not very well-known in the optimization community. This approach provides some new insights on duality concepts for integer programs, and also permits to retrieve and shed new light on some well-known results. For instance, Gomory relaxations and the abstract superadditive dual of integer programs are re-interpreted in this algebraic approach.This book will serve graduate students and researchers in applied mathematics, optimization, operations research and computer science. Due to the substantial practical importance of some presented problems, researchers in other areas will also find this book useful., Springer-Verlag Gmbh
Rheinberg-Buch.de
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ISBN: 9780387094144
ID: 9780387094144
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. Linear and Integer Programming vs Linear Integration and Counting: 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., Springer-Verlag Gmbh
Rheinberg-Buch.de
Ebook, Englisch, Neuware Shipping costs:Ab 20¤ Versandkostenfrei in Deutschland, Sofort lieferbar, DE. (EUR 0.00)
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2009
ISBN: 0387094148
ID: 9780387094144
In englischer Sprache. Verlag: Springer New York, 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. PC-PDF, 168 Seiten, XIV Seiten, 168 Seiten, [GR: 9629 - Nonbooks, PBS / Mathematik/Sonstiges], [SW: - Mathematik], [Ausgabe: 2009][PU:Springer New York], [PU: Springer]
Libreka.de |
2009, ISBN: 9780387094144
ID: 21671102
A Duality Viewpoint, [ED: 1], Auflage, eBook Download (PDF), eBooks, [PU: Springer-Verlag]
Lehmanns.de
Shipping costs:Download sofort lieferbar, , Versandkostenfrei innerhalb der BRD (EUR 0.00)
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2009, ISBN: 9780387094144
ID: 21671102
A Duality Viewpoint, [ED: 2009], eBook Download (PDF), eBooks, [PU: Springer New York]
Lehmanns.de
Shipping costs:Download sofort lieferbar, , Versandkostenfrei innerhalb der BRD (EUR 0.00)
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Author: | |
Title: | Linear and Integer Programming vs Linear Integration and Counting |
ISBN: | 0387094148 |
Details of the book - Linear and Integer Programming vs Linear Integration and Counting
EAN (ISBN-13): 9780387094144
ISBN (ISBN-10): 0387094148
Publishing year: 2009
Publisher: Springer New York
168 Pages
Language: eng/Englisch
Book in our database since 26.04.2007 16:03:19
Book found last time on 19.02.2016 00:31:37
ISBN/EAN: 0387094148
ISBN - alternate spelling:
0-387-09414-8, 978-0-387-09414-4
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