Who Invented the Interior - Point Method ?

Thomas Edison is regarded by many as the greatest inventor in American history. While most people know that he invented the first long-burning incandescent light bulb and the phonograph, the claim is based more generally on the 1093 patents he was granted. The assumption is that the person receiving a patent is legally certified as the inventor of the device which is the subject of the patent. The invention of the stored program computer during and in the period immediately following World War II vastly expanded the range of practical mathematical problems which could be solved numerically. A particular form of problem which received great interest is the linear programming problem, which allocates resources optimally subject to constraints. George Dantzig’s development of the simplex method [5], provided the computational tool still prominent in the field today for the solution of these problems. Continuous development of variants of the simplex method has led to contemporary codes that are quite efficient for many very large problems. However, as the simplex method proceeds from one vertex of the feasible region defined by the constraints to a neighboring vertex, the combinatorial analysis indicates it can be quite inefficient for some problems. In [14], Klee and Minty showed that, in the worst case, the method has exponential complexity in the size of the problem. The question that then presented itself is whether there is another algorithm for linear programming which has polynomial complexity. This question was first answered positively in 1979 by Khachian [13], who adapted the ellipsoid method of Shor [18] and showed that the complexity of the resulting algorithm was polynomial of order (