ArcLP: A Matlab implementation of an $\mathcal{O}(\sqrt{n}L)$ arc-search infeasible interior-point algorithm for linear programming

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.

Source: arXiv:2607.29673v1 - http://arxiv.org/abs/2607.29673v1 PDF: https://arxiv.org/pdf/2607.29673v1 Original Link: http://arxiv.org/abs/2607.29673v1