On the primal–dual method of interior point programming

In this work, we deal with the formulation of the primal–dual interior-point method both for linear and convex quadratic programming. Recently, it was shown that it cannot be viewed as a damped Newton method applied to the Karush–Kuhn–Tucker conditions for the primal logarithmic barrier function problem. We extend this result in two directions. Firstly, we show that it cannot be viewed as a damped Newton method applied to the Karush–Kuhn–Tucker conditions for the dual logarithmic barrier function problem. Secondly, we show that this is true also for convex quadratic programming. Finally, we show a similar relation between the standard formulation of the Karush–Kuhn–Tucker perturbed conditions which all primal–dual methods use to derive their search directions, and a different parametrization of these conditions.