Jean-Bernard Lasserre

Linear and Integer Programming vs Linear Integration and Counting (eBook, PDF)

A Duality Viewpoint

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 168
• Erscheinungstermin: 21. April 2009
• Englisch
• ISBN-13: 9780387094144
• Artikelnr.: 37287633

Inhaltsangabe

Preface. Introduction.- Part I. Linear Integration and Linear Programming. The Linear Integration Problem I. Comparing the Continuous Problems P and I.- Part II. Linear Counting and Integer Programming- The Linear Counting Problem I(d). Relating the Discrete Problems P(d) and I(d) with P.- Part III. Duality. Duality and Gomory Relaxations. Barvinok s Counting Algorithm and Gomory Relaxations. A Discrete Farkas Lemma. The Integer Hull of a Convex Rational Polytope. Duality and Superadditive Functions.- Appendix: Legendre-Fenchel, Laplace, Cramer, and Z Transforms. References. Glossary.- Index.

Rezensionen

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)