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 eeect that weighting the central path has on its limiting derivatives has not been fully explored. We show that when there is a unique dual solution, 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.