Convergence analysis of an interior point method in convex programming, regular constraint case

We study the convergence properties of a previously proposed algorithm in the context of solving a class of smooth nonlinear convex optimization problems. With some mild assumptions, it is shown that the algorithm has global convergence with guaranteed accuracy upon termination. Further, an upper bound for the local rate of convergence is derived. It rigorously justifies the efficiency of the algorithm in spite of the fact that the bound is in general conservative.