50 Years of Integer Programming 1958-2008: From the Early Years to the State-of-the-Art / Edition 1

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Overview

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 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.

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Editorial Reviews

From the Publisher

From the reviews:

“This volume originates from the 12th Combinatorial Optimization Workshop in Aussois, 2008, where 50 years of integer programming were celebrated. It describes the history and the present state of integer programming. The volume consists of four parts … . This volume is a precious account of the history and the current state of integer programming.” (Rainer Burkard, Mathematical Reviews, Issue 2011 f)

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Product Details

  • ISBN-13: 9783540682745
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 1/26/2010
  • Edition description: 2010
  • Edition number: 1
  • Pages: 804
  • Product dimensions: 6.50 (w) x 9.40 (h) x 1.70 (d)

Table of 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.

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