"On the Local Behavior of an Interior Point Method for Nonlinear Programming"
R. Byrd, G. Liu, J. Nocedal
Numerical Analysis , eds. D.F. Griffiths and D.J. Higham, pp.37-56 (1997) Addison Wesley Longman
We study the local convergence of a primal-dual interior point method for nonlinear programming. A linearly convergent version of this algorithm has been shown in  to be capable of solving large and difficult non-convex problems. But for the algorithm to reach its full potential, it must converge rapidly to the solution. In this paper we describe how to design the algorithm so that it converges superlinearly on regular problems.