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

by Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank

Overview

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.

Product Details

ISBN-13:	9783662501818
Publisher:	Springer Berlin Heidelberg
Publication date:	02/09/2011
Edition description:	Softcover reprint of the original 1st ed. 2010
Pages:	804
Product dimensions:	6.10(w) x 9.25(h) x (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.- TheGroup-Theoretic Approach in Mixed Integer Programming.

Editorial Reviews

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)

From the Publisher