Abstract:

In joint work with Jean-Pierre Dedieu and Gregorio Malajovich we study the average curvature of the central path of linear programming theory. We prove on average that the curvature is linear in the number of variables of the problem. This average result should be contrasted with the recent results of Deza, Nematollahi, Peyghami and Terlaki showing that the central path may visit all the vertices of the Klee-Minty cube. Our tools are: integral geometry, Bezout's theorem and some ideas of dyanmical systems theory.