50 Years of Integer Programming 1958-2008

From the Early Years to the State-of-the-Art

  • Michael Jünger
  • Thomas M. Liebling
  • Denis Naddef
  • George L. Nemhauser
  • William R. Pulleyblank
  • Gerhard Reinelt
  • Giovanni Rinaldi
  • Laurence A. Wolsey

Table of contents

  1. Front Matter
    Pages i-xvi
  2. The Early Years

    1. Front Matter
      Pages 1-6
    2. Vašek Chvátal, William Cook, George B. Dantzig, Delbert R. Fulkerson, Selmer M. Johnson
      Pages 7-28
    3. Alan J. Hoffman, Joseph B. Kruskal
      Pages 49-76
    4. Ailsa H. Land, Alison G. Doig
      Pages 105-132
    5. Michel Balinski
      Pages 133-197
    6. Jack Edmonds
      Pages 199-217
    7. Richard M. Karp
      Pages 219-241
    8. Arthur M. Geoffrion
      Pages 243-281
    9. Egon Balas
      Pages 283-340
  3. From the Beginnings to the State-of-the-Art

    1. Front Matter
      Pages 341-342
    2. Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli
      Pages 343-385
    3. François Vanderbeck, Laurence A. Wolsey
      Pages 431-502
  4. Current Topics

    1. Front Matter
      Pages 503-504
    2. Friedrich Eisenbrand
      Pages 505-559
    3. Raymond Hemmecke, Matthias Köppe, Jon Lee, Robert Weismantel
      Pages 561-618
    4. Andrea Lodi
      Pages 619-645
    5. François Margot
      Pages 647-686
    6. Jean-Philippe P. Richard, Santanu S. Dey
      Pages 727-801
  5. Back Matter
    Pages 1-2

About this book


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.


(mixed) integer linear programming Partition algorithms combinatorial optimization geometry linear optimization mathematical methods of operations reearch mathematical programming nonlinear integer programming operations research optimization s

Editors and affiliations

  • Michael Jünger
    • 1
  • Thomas M. Liebling
    • 2
  • Denis Naddef
    • 3
  • George L. Nemhauser
    • 4
  • William R. Pulleyblank
    • 5
  • Gerhard Reinelt
    • 6
  • Giovanni Rinaldi
    • 7
  • Laurence A. Wolsey
    • 8
  1. 1.Inst. InformatikUniversität KölnKölnGermany
  2. 2.Fac. Sciences de Base (FSB)Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.EnsimagInstitut Polytechnique de GrenobleGrenoble CX 1France
  4. 4.School of Industrial &Georgia Institute of TechnologyAtlantaU.S.A.
  5. 5.IBM CorporationSomersU.S.A.
  6. 6.Inst. InformatikUniversität HeidelbergHeidelbergGermany
  7. 7.ed InformaticaCNR - Ist. Analisi dei SistemiRomaItaly
  8. 8.Center for Operations Reserach &Université Catholique de LouvainLeuvenBelgium

Bibliographic information