THE MEHROTRA PREDICTOR-CORRECTOR INTERIOR-POINT METHOD AS A PERTURBEDCOMPOSITE NEWTON METHOD

It is well known that the celebrated Kojima-Mizuno-Yoshise primal-dual interior-point method for linear programming can be viewed as a dampe d perturbed Newton's method. Recently, Mehrotra suggested a predictor- corrector variant of this method. It is currently the interior-point m ethod of choice for linear programming. The simplified Newton method, at the expense of fast convergence, reduces the work required by Newto n's method by reusing the initial Jacobian matrix. The composite Newto n method attempts to balance the trade-off between expense and fast co nvergence by composing one Newton step with one simplified Newton step . In this work we demonstrate that if the Newton component in the Koji ma-Mizuno-Yoshise primal-dual method is replaced with a composite Newt on component, then the resulting method is the Mehrotra predictor-corr ector method.