In this paper, we propose a theoretical framework of a predictor-corrector interior-point method for linear optimization based on the one-norm wide neighborhood of the central path, focusing on infeasible corrector steps. Here, we call the predictor-infeasible corrector algorithm. At each iteration, the proposed algorithm computes an infeasible corrector step in addition to the Ai-Zhang search directions and considers the Newton direction as a linear combination of these directions. We represent the complexity analysis of the algorithm and conclude that its iteration bound is \({\mathcal {O}}(n\log \varepsilon ^{-1})\). To our knowledge, this is the best complexity result up to now for infeasible interior-point methods based on these kinds of search directions. The complexity bound obtained here is the same as small neighborhood infeasible interior point algorithms.

在本文中，我们提出了一种基于中心路径的一个标准宽邻域的线性优化预测器-校正器内点方法的理论框架，重点是不可行的校正器步骤。在这里，我们将预测器不可行的校正器算法。在每次迭代中，除了Ai-Zhang搜索方向外，所提出的算法还计算不可行的校正器步骤，并将牛顿方向视为这些方向的线性组合。我们表示该算法的复杂度分析，并得出其迭代边界为\（{\ mathcal {O}}（n \ log \ varepsilon ^ {-1}）\）。据我们所知，这是迄今为止基于这些搜索方向的不可行内点方法的最佳复杂性结果。此处获得的复杂度界限与小邻域不可行内点算法相同。