We consider the classical duality operators for convex objects such as the polar of a convex set containing the origin, the dual norm, the Fenchel-transform of a convex function and the conjugate of a convex cone. We give a new, sharper, unified treatment of the theory of these operators,...

In this paper we study the properties of the analytic central path of a semidefinite programming problem under perturbation of a set of input parameters. Specifically, we analyze the behavior of solutions on the central path with respect to changes on the right hand side of the constraints,...

In this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face is...