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

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


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, Grard Cornujols, 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 Kppe, 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 Programming
Integer 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.

Table of contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-6
Solution of a Large-Scale Traveling-Salesman Problem....Pages 7-28
The Hungarian Method for the Assignment Problem....Pages 29-47
Integral Boundary Points of Convex Polyhedra....Pages 49-76
Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem....Pages 77-103
An Automatic Method for Solving Discrete Programming Problems....Pages 105-132
Integer Programming: Methods, Uses, Computation....Pages 133-197
Matroid Partition....Pages 199-217
Reducibility Among Combinatorial Problems....Pages 219-241
Lagrangian Relaxation for Integer Programming....Pages 243-281
Disjunctive Programming....Pages 283-340
Front Matter....Pages 341-342
Polyhedral Approaches to Mixed Integer Linear Programming....Pages 343-385
Fifty-Plus Years of Combinatorial Integer Programming....Pages 387-430
Reformulation and Decomposition of Integer Programs....Pages 431-502
Front Matter....Pages 503-504
Integer Programming and Algorithmic Geometry of Numbers....Pages 505-559
Nonlinear Integer Programming....Pages 561-618
Mixed Integer Programming Computation....Pages 619-645
Symmetry in Integer Linear Programming....Pages 647-686
Semidefinite Relaxations for Integer Programming....Pages 687-726
The Group-Theoretic Approach in Mixed Integer Programming....Pages 727-801
Back Matter....Pages 1-2


  • Author: Vaek Chvtal, William Cook, George B. Dantzig, Delbert R. Fulkerson, Selmer M. Johnson (auth.), Michael Jnger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, Laurence A. Wolsey (eds.)
  • Edition: 1
  • Publication Date: 2010
  • Publisher: Springer-Verlag Berlin Heidelberg
  • ISBN-10: 3540682740
  • ISBN-13: 9783540682745
  • Pages: 811
  • Format: pdf
  • Size: 5.6M
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