Homotopy techniques in linear programming

In this note, we consider the solution of a linear program, using suitably adapted homotopy techniques of nonlinear programming and equation solving that move through the interior of the polytope of feasible solutions. The homotopy is defined by means of a quadratic regularizing term in an appropriate metric. We also briefly discuss algorithmic implications and connections with the affine variant of Karmarkar's method.This is a revised version of a paper previously entitled Karmarkar's Method and Homotopies with Restarts.