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 keyhistorical 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.
"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 programming. In addition it gives an in depth and great historical perspective of the huge amount of research and development that has taken place in the field of integer programming over a period of 50 years." (Hans W. Ittmann, IFORS News, Vol. 12 (2), June, 2018)
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. Thevolume 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)
