Transformations of dual problem and decreasing dimensions in linear programming

Abstract

We investigate behavior of the potential function in a modification of the Mehrotra's primal-dual algorithm. This modification reduces dimensions of the problem and eliminates need for the finite termination algorithm. Numerical results on some examples from the Netlib test set are provided. We also regard problems about applying a stabilization procedure proposed by Kovačević-Vujčić and Ašić in the Mehrotra's primal dual interior-point algorithm for linear programming. Transformations of the dual problem required for the application of the stabilization procedure are considered.