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 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. Key words: analytic central path, computational economics, sensitivity analysis AMS subject classification: 90C31,49K40,15A60 1 Department of Mathematics, University of Colorado at Denver, U.S.A. 2 Department of Economics, Mathematics, and Statistics, University of Windsor, 401 Sunset Avenue, Windsor, Ontario, Canada N9B 3P4 1 Introduction Consider the standard form primal linear programming problem (LP) min f cx : Ax = b; x 0 g and its associated ..