Interior-point methods via self-concordance or relative lipschitz condition

In this article we present a simple introduction to the notion of self-concordance and its implications for convex programming. We consider certain interior-point methods for solving convex programs Starting from a straightforward derivation of sufficient conditions that allow the formulation of a polynomial time interior-point method, we give an outline of the method of centers. Our presentation includes a complete analysis of the method as well as some improved results on ellipsoidal approximations of the feasible set