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.

翻译：不精确内点法是内点法的一种，它通过非精确求解线性方程组来获得搜索方向。另一方面，弧搜索内点法通过每次迭代求解两个线性方程组得到的椭圆弧来逼近中心路径，而传统的线搜索内点法只求解一个线性系统。因此，在弧搜索内点法中，线性方程组的非精确解所带来的改进比传统内点法更为显著。本文提出了一种不精确不可行弧搜索内点法。通过收敛性分析，我们证明了该方法是一种多项式时间算法。采用共轭梯度法的数值实验表明，与现有方法相比，所提方法能减少基准问题的迭代次数；对于超过70%的问题，迭代次数减少至三分之二。