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50 years of integer programming, 1958-2008 : from the early years to the state-of-the-art

Author: M Jünger
Publisher: Heidelberg ; New York : Springer, ©2010.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Summary:
In 1958, Ralph E. Gomory transformed the field of integer programming when he published a short paper that described his cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In January of 2008, to commemorate the anniversary of Gomory's seminal paper, a special session celebrating fifty years of integer programming was  Read more...
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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: Print version:
50 years of integer programming 1958-2008.
Heidelberg : Springer, ©2010
(OCoLC)651613047
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: M Jünger
ISBN: 9783540682790 3540682791
OCLC Number: 466224950
Notes: Selected conference papers from the 12th Combinatorial Optimization Workshop AUSSOIS 2008 held in Aussois, France, January 7-11, 2008.
Description: 1 online resource (xx, 803 pages) : illustrations
Contents: I The Early Years --
Solution of a Large-Scale Traveling-Salesman Problem --
The Hungarian Method for the Assignment Problem --
Integral Boundary Points of Convex Polyhedra --
Outline of an Algorithm for Integer Solutions to Linear Programs An Algorithm for the Mixed Integer Problem --
An Automatic Method for Solving Discrete Programming Problems --
Integer Programming: Methods, Uses, Computation --
Matroid Partition --
Reducibility Among Combinatorial Problems --
Lagrangian Relaxation for Integer Programming --
Disjunctive Programming --
II From the Beginnings to the State-of-the-Art --
Polyhedral Approaches to Mixed Integer Linear Programming --
Fifty-Plus Years of Combinatorial Integer Programming --
Reformulation and Decomposition of Integer Programs --
III Current Topics --
Integer Programming and Algorithmic Geometry of Numbers --
Nonlinear Integer Programming --
Mixed Integer Programming Computation --
Symmetry in Integer Linear Programming --
Semidefinite Relaxations for Integer Programming --
The Group-Theoretic Approach in Mixed Integer Programming.
Other Titles: Fifty years of integer programming, 1958-2008
Responsibility: Michael Jünger [and others], editors.

Abstract:

50 Years of Integer Programming features talks and panel discussions from the Aussois workshop in 2008, commemorating the cutting-plane algorithm, which transformed the field. Key topics of integer  Read more...

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"It is a concise, yet voluminous, book giving the theoretical, algorithmic and computational aspects of integer programming. ... The book provides and serves as an excellent introduction to integer Read more...

 
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   schema:description "In 1958, Ralph E. Gomory transformed the field of integer programming when he published a short paper that described his cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In January of 2008, to commemorate the anniversary of Gomory's seminal paper, a special session celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. This book is based on the material presented during this session. 50 Years of Integer Programming offers an account of featured talks at the 2008 Aussois workshop, namely- Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli: Polyhedral Approaches to Mixed Integer Linear Programming- William Cook: 50+ Years of Combinatorial Integer Programming - Francois Vanderbeck and Laurence A. Wolsey: Reformulation and Decomposition of Integer Programs The book contains reprints of key historical articles together with new introductions and historical perspectives by the authors: Egon Balas, Michel Balinski, Jack Edmonds, Ralph E. Gomory, Arthur M. Geoffrion, Alan J. Hoffman & Joseph B. Kruskal, Richard M. Karp, Harold W. Kuhn, and Ailsa H. Land & Alison G. Doig. It also contains written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community: - Friedrich Eisenbrand: Integer Programming and Algorithmic Geometry of Numbers- Raymond Hemmecke, Matthias Köppe, Jon Lee, and Robert Weismantel: Nonlinear Integer Programming- Andrea Lodi: Mixed Integer Programming Computation- Francois Margot: Symmetry in Integer Linear Programming- Franz Rendl: Semidefinite Relaxations for Integer Programming - Jean-Philippe P. Richard and Santanu S. Dey: The Group-Theoretic Approach to Mixed Integer ProgrammingInteger programming holds great promise for the future, and continues to build on its foundations. Indeed, Gomory's finite cutting-plane method for the pure integer case is currently being reexamined and is showing new promise as a practical computational method. This book is a uniquely useful celebration of the past, present and future of this important and active field. Ideal for students and researchers in mathematics, computer science and operations research, it exposes mathematical optimization, in particular integer programming and combinatorial optimization, to a broad audience."@en ;
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