AI 中文总结
本文实现了具有最优O(√n L)多项式界的线性规划弧搜索不可行内点算法，经Netlib基准测试，其计算性能与Mehrotra预测-校正算法相当，且能求解大规模问题。
AI 中文摘要
本文提出了线性规划（LP）的弧搜索不可行内点算法的Matlab实现，该算法已被证明具有O(√n L)的多项式界，是所有LP内点算法中最优的。文中讨论了软件架构和主要功能，通过一个简单示例说明了其易用性，总结了关键策略。该软件在PC和Linux上对广泛使用的Netlib基准标准形式线性规划问题进行了大量测试，确保了软件质量。部分基准测试问题包含数万个约束和数十万个变量，对于所有测试问题，该代码均找到了最优解。将数值结果与流行的Mehrotra预测-校正算法的结果进行了比较，得出结论：所实现的算法不仅具有最优的多项式界，而且与流行的Mehrotra预测-校正算法相比，计算性能具有竞争力。
英文摘要
This paper presents a Matlab implementation of an arc-search infeasible interior point algorithm for linear programming (LP), which has a proven polynomial bound of $\mathcal{O}(\sqrt{n}L)$, the best among all interior-point algorithms for LP. Software architecture and major functions are discussed. Its ease of use is described by a simple example. Crucial strategies are summarized. Quality of the software is assured because this software has been extensively tested on both PC and Linux for the widely used Netlib benchmark linear programming problems in standard form. Some benchmark test problems involve tens of thousands of constraints and hundreds of thousands of variables. For all tested problems, the code found the optimal solution. The numerical results have been compared to those obtained by the popular Mehrotra's predictor-corrector algorithm. We conclude that the implemented algorithm not only has the best polynomial bound but also is computationally competitive compared to the popular Mehrotra's predictor-corrector algorithm.
Comments12 Pages
Journal refJournal of Open Research Software 2026
DOI：10.5334/jors.674
