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OverviewInteger 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. Full Product DetailsAuthor: Jean-Bernard LasserrePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of hardcover 1st ed. 2009 Dimensions: Width: 17.80cm , Height: 0.90cm , Length: 23.50cm Weight: 0.360kg ISBN: 9781441918536ISBN 10: 1441918531 Pages: 168 Publication Date: 15 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. Table of ContentsI 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.ReviewsFrom the reviews: Lasserre has produced a fascinating slim ! monograph (much of the work his own) looking at the parallels between linear (respectively integer) programming on the one hand and integration (respectively integer counting) problems on the other hand. ! An appendix on various transforms a hundred references and a brief index complete the work which is a welcome addition to an important set of topics. (J. Borwein, Mathematical Reviews, Issue 2010 f) This book is devoted to analysing four important problems: integer programming problem, linear programming problem, linear integration problem, and linear counting problem. ! a very specialized book on the integer programming problem and its dual variants. ! can be very helpful for researchers working in developing algorithms for the integer programming problem which is a formidable challenging problem. This is a clear and well-written book ! . (E. Almehdawe, Journal of the Operational Research Society, Vol. 61 (12), 2010) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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