Global and polynomial-time convergence of an infeasible-interior-point algorithm using inexact computation

Abstract

In this paper, we propose an infeasible-interior-point algorithm for solving a primal-dual linear programming problem. The algorithm uses inexact computations for solving a linear system of equations at each iteration. Under a very mild assumption on the inexactness we show that the algorithm finds an approximate solution of the linear program whenever the primal-dual linear programming problem is feasible. The assumption on the inexact computation is satisfied if the approximation to the solution of the linear system is just a little bit better than the trivial approximation 0.