A simple proof of a primal affine scaling method

This paper presents a simpler proof of the result of Tsuchiya and Muramatsu on the convergence of the primal affine scaling method. It shows that the primal sequence generated by the method converges to the interior of the optimum face and the dual sequence to the analytic center of the optimal dual face, when the step size implemented in the procedure is bounded by 2/3. The paper also proves the optimality of the limit of the primal sequence for a slightly larger step size of 2q/(3q-1), where q is the number of zero variables in the limit. It shows this by proving the dual feasibility of a cluster point of the dual sequence.