Asymptotic analysis of a path-following barrier method for linearly constrained convex problems *

In the present paper the logarithmic barrier method applied to the linearly constrained convex optimization problems is studied from the view point of classical path-following algorithms. In particular, the radius of convergence of Newton's method which depends on the barrier parameter itself is estimated in standard norms, being independent of the parameter, without explicitly using self-concordance properties. The obtained results establish a parameter selection rule which guarantees the overall convergence of a barrier technique with only one Newton step at each parameter level and the complexity of the method can be estimated.