An inexact potential reduction method for linear programming
  A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand side. For the new system an implementable condition is formulated that controls the relative error in the solution. Based on this condition, a feasible and an infeasible potential reduction method are described which retain the convergence and complexity bounds known for exact directions. 
Lukas Schork and Jacek Gondzio
math.OC