On the Convergence of an Inexact Primal-Dual Interior Point Method for Linear Programming

Abstract

The inexact primal-dual interior point method which is discussed in this paper chooses a new iterate along an approximation to the Newton direction. The method is the Kojima, Megiddo, andMizuno globally convergent infeasible interior point algorithm. The inexact variation is shown to have the same convergence properties accepting a residue in both the primal and dual Newton step equation also for feasible iterates.