A potential-reduction variant of Renegar's short-step path-following method for linear programming

Abstract

We propose a new polynomial potential-reduction method for linear programming, which can also be seen as a large-step path-following method. We do an (approximate) linesearch along the Newton direction with respect to Renegar's strictly convex potential function if the iterate is far away from the central trajectory. If the iterate lies close to the trajectory, we update the lower bound for the optimal value. Dependent on this updating scheme, the iteration bound can be proved to be O( n L) or O( nL). Our method differs from the recently published potential-reduction methods in the choice of the potential function and the search direction.