50 Years of Integer Programming 1958-2008 (eBook)

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 (Herausgeber)

eBook Download: PDF

2009 | 2010
XX, 804 Seiten
Springer Berlin (Verlag)
978-3-540-68279-0 (ISBN)

Infos

In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop.

It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience.

Inhalt

About the Cover Illustration 9
Contents 12
Part I The Early Years 18
1 Solution of a Large-Scale Traveling-Salesman Problem 24
2 The Hungarian Method for the Assignment Problem 46
3 Integral Boundary Points of Convex Polyhedra 65
4 Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem 93
5 An Automatic Method for Solving Discrete Programming Problems 120
6 Integer Programming: Methods, Uses, Computation 148
7 Matroid Partition 213
8 Reducibility Among Combinatorial Problems 232
9 Lagrangian Relaxation for Integer Programming 255
10 Disjunctive Programming 294
Part II From the Beginnings to the State- of- the- Art 352
11 Polyhedral Approaches to Mixed Integer Linear Programming 354
12 Fifty-Plus Years of Combinatorial Integer Programming 397
13 Reformulation and Decomposition of Integer Programs 441
Part III Current Topics 513
14 Integer Programming and Algorithmic Geometry of Numbers 515
15 Nonlinear Integer Programming 570
16 Mixed Integer Programming Computation 628
17 Symmetry in Integer Linear Programming 655
18 Semidefinite Relaxations for Integer Programming 695
19 The Group-Theoretic Approach in Mixed Integer Programming 735
Part IV DVD-Video / DVD-ROM 810

Produkt-Details

• Erscheint lt. Verlag: 6.11.2009
• Zusatzinfo: XX, 804 p. 151 illus., 52 illus. in color.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Schlagworte: algorithms • combinatorial optimization • combinatorics • Geometry • linear optimization • mathematical methods of operations reearch • Mathematical Programming • (mixed) integer linear programming • nonlinear integer programming • Operations Research • Optimization • Partition • S • semidefinite programming
• ISBN-10: 3-540-68279-1 / 3540682791
• ISBN-13: 978-3-540-68279-0 / 9783540682790