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Linear and Integer Programming vs Linear Integration and Counting

A Duality Viewpoint

Medium: Buch
ISBN: 978-0-387-09413-7
Verlag: Humana
Erscheinungstermin: 28.04.2009
Lieferfrist: bis zu 10 Tage

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.


Produkteigenschaften


  • Artikelnummer: 9780387094137
  • Medium: Buch
  • ISBN: 978-0-387-09413-7
  • Verlag: Humana
  • Erscheinungstermin: 28.04.2009
  • Sprache(n): Englisch
  • Auflage: 2009
  • Serie: Springer Series in Operations Research and Financial Engineering
  • Produktform: Gebunden, HC runder Rücken kaschiert
  • Gewicht: 514 g
  • Seiten: 168
  • Format (B x H x T): 183 x 241 x 16 mm
  • Ausgabetyp: Kein, Unbekannt
Autoren/Hrsg.

Autoren

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.