50 Years of Integer Programming 1958-2008

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November 2009



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.


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.



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)
EAN: 9783540682790
Untertitel: From the Early Years to the State-of-the-Art. 2010. Auflage. Sprache: Englisch. Dateigröße in MByte: 38.
Verlag: Springer Berlin Heidelberg
Erscheinungsdatum: November 2009
Format: pdf eBook
Kopierschutz: Adobe DRM
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