George B. Dantzig [chapter]

Saul I. Gass
2011 International Series in Operations Research and Management Science  
The final test of a theory is its capacity to solve the problems which originated it. This work is concerned with the theory and solution of linear inequality systems. . . . The viewpoint of this work is constructive. It reflects the beginning of a theory sufficiently powerful to cope with some of the challenging decision problems upon which it was founded. S o says George B. Dantzig in the preface to his book, Linear Programming and Extensions, a now classic work published in 1963, some
more » ... years after his formulation of the linear programming problem and discovery of the simplex algorithm for its solution. The three passages quoted above represent essential components of Dantzig's outlook on linear programming and, indeed, on mathematics generally. The first expresses his belief in the importance of real world problems as an inspiration for the development of mathematical theory, not for its own sake, but as a means to solving important practical problems. The second statement is based on the theoretical fact that although a linear programming problem, is, prima facie, concerned with constrained optimization, it is really all about solving a linear inequality system. The third statement reveals Dantzig's conviction that constructive
doi:10.1007/978-1-4419-6281-2_13 fatcat:cc4lfxmnhfbyfibwc3v7tmxqjq