Primal-dual interior point methods have been intensively studied in the past two decades. However, it remains touchy to ensure both global convergence and fast asymptotic efficiency. Log barrier methods naturally possess the global convergence (to stationary points) property but one has to resort to extrapolations to enhance their asymptotic behavior. We will present recent developments about high order path (primal) following methods. Moreover, we will present some evidence that such approaches may be efficient even when no constraint qualification holds and the KKT multiplier set is empty.
Group for Research in Decision Analysis