Achievable potential reductions in the method of Kojima et al. in the case of linear programming

Kojima et al proposed a primal-dual interior point method, based on potential reduction for solving the linear complementarity problem, and they derived an iteration bound. In the derivation of this bound they used equal step sizes in the primal and the dual space, and they showed that taking the step size equal to 0.4 the potential reduction, is at least 0.2. This paper specializes to the case of linear programming and shows that the latter constant can be improved to 0.267. Further, admitting different step sizes in both spaces. The paper shows that a further improvement of this constant to 0.345 is possible. Furthermore, for the case of equal step sizes it is shown that the duality gap is monotically decreasing.