Uniform bounds on the limiting and marginal derivatives of the analytic center solution over a set of normalized weights

While properties of the weighted central path for linear and non-linear programs have been studied for years, the effect that weighting the central path has on its limiting derivatives has not been fully explored. We show that the limiting derivatives of the central path for a linear program are uniformly bounded over a set of normalized weights. Consequently, this allows a similar bound for the marginal derivatives of the analytic center solution with respect to changes in the right-hand side.