50 Years of Integer Programming 1958-2008: From the Early by Michael Jünger, Thomas M. Liebling, Denis Naddef, George L.

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

In 1958, Ralph E. Gomory reworked the sector of integer programming whilst he released a paper that defined a cutting-plane set of rules for natural integer courses and introduced that the strategy may be sophisticated to provide a finite set of rules for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a unique workshop celebrating fifty years of integer programming was once held in Aussois, France, as a part of the twelfth Combinatorial Optimization Workshop. It comprises reprints of key historic articles and written models of survey lectures on six of the most popular themes within the box by way of extraordinary participants of the integer programming neighborhood. important for an individual in arithmetic, computing device technological know-how and operations study, this ebook exposes mathematical optimization, particularly integer programming and combinatorial optimization, to a extensive viewers.

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The formulation of the assignment problem as a linear program was well known, but a 10 by 10 assignment problem has 100 variables in its primal statement and 100 constraints in the dual and so was too large for the SWAC to solve as a linear program. The SEAC (Standard Eastern Automatic Computer), housed in the National Bureau of Standards in Washington, could solve linear programs with about 25 variables and 25 constraints. The SEAC had a liquid mercury memory system which was extremely limiting.

Alan J. com Joseph B. net M. Jünger et al.

Campus. I was supported by the National Bureau of Standards and shared an office with Ted Motzkin, a pioneer in the theory of inequalities and one of the most scholarly mathematicians I have ever known. I had no fixed duties and spent the summer working on subjects that were of interest to me at the time, such as the traveling salesman problem and the assignment problem. The Institute for Numerical Analysis was the home of the SWAC (Standards Western Automatic Computer), which had been designed by Harry Huskey and had a memory of 256 words of 40 bits each on 40 Williamson tubes.

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