An inexact infeasible arc-search interior-point method for linear programming problems

Inexact interior-point methods (IPMs) are a type of interior-point methods that inexactly solve the linear equation system for obtaining the search direction. On the other hand, arc-search IPMs approximate the central path with an ellipsoidal arc obtained by solving two linear equation systems in each iteration, while conventional line-search IPMs solve one linear system, therefore, the improvement due to the inexact solutions of the linear equation systems can be more beneficial in arc-search IPMs than conventional IPMs. In this paper, we propose an inexact infeasible arc-search interior-point method. We establish that the proposed method is a polynomial-time algorithm through its convergence analysis. The numerical experiments with the conjugate gradient method show that the proposed method can reduce the number of iterations compared to an existing method for benchmark problems; the numbers of iterations are reduced to two-thirds for more than 70% of the problems.