  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.
