The relation between the path of centers and Smale's regularization of the linear programming problem

Abstract

Smale proposed a framework for applying Newton's method to the linear programming problem. It is shown that his method is closely related to recent interior point methods, in the sense that it also traces the path of centers, even though the tracing is done outside the affine hull of the feasible domain. Also, an equivalence of the fundamental theorems is pointed out. © 1991.