A globally and superlinearly convergent potential reduction interior point method for convex programming

We consider an interior point algorithm for convex programming in which the steps are generated by using a primal-dual ane scaling technique. A \local " variant of the algorithm is shown to have superlinear convergence with q-order up to (but not including) 2. The technique is embedded in a potential reduction algorithm and the resulting method is shown to be globally and superlinearly convergent. An important feature of the convergence analysis is its use of a novel strict interiority condition, which generalizes the usual conical neighborhood of the central path.