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OverviewThis 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 Vergne's 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. Full Product DetailsAuthor: Jean-Bernard LasserrePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2009 ed. Dimensions: Width: 17.80cm , Height: 1.50cm , Length: 23.50cm Weight: 0.514kg ISBN: 9780387094137ISBN 10: 038709413 Pages: 168 Publication Date: 28 April 2009 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. 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) From 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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