Analytic Central Path, Sensitivity Analysis and Parametric Linear Programming

In this paper we consider properties of the central path and the analytic center of the optimalface in the context of parametric linear programming. We first show that if the right-hand sidevector of a standard linear program is perturbed, then the analytic center of the optimal face isone-side differentiable with respect to the perturbation parameter. In that case we also showthat the whole analytic central path shifts in a uniform fashion. When the objective vector isperturbed, we show that the last part of the analytic central pathis tangent to a central path defined on the optimal face of the original problem.