{"title":"Geometric programming for multilinear systems with nonsingular M-tensors","authors":"Haibin Chen , Guanglu Zhou , Hong Yan","doi":"10.1016/j.aml.2025.109462","DOIUrl":null,"url":null,"abstract":"<div><div>We consider multilinear systems which arise in various applications, such as data mining and numerical differential equations. In this paper, we show that the multilinear system with a nonsingular <span><math><mi>M</mi></math></span>-tensor can be formulated equivalently into a geometric programming (GP) problem which can be solved by the barrier-based interior point method with a worst-case polynomial-time complexity. To the best of our knowledge, there is not a complexity analysis for the existing algorithms of the multilinear systems. Numerical results are reported to show the efficiency of the proposed GP method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109462"},"PeriodicalIF":2.9000,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925000096","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider multilinear systems which arise in various applications, such as data mining and numerical differential equations. In this paper, we show that the multilinear system with a nonsingular -tensor can be formulated equivalently into a geometric programming (GP) problem which can be solved by the barrier-based interior point method with a worst-case polynomial-time complexity. To the best of our knowledge, there is not a complexity analysis for the existing algorithms of the multilinear systems. Numerical results are reported to show the efficiency of the proposed GP method.
我们考虑了在数据挖掘和数值微分方程等各种应用中出现的多线性系统。在本文中，我们展示了具有非正弦 M 张量的多线性系统可以等价地表述为一个几何程序设计（GP）问题，该问题可以通过基于障碍的内点法求解，并具有最坏情况下的多项式时间复杂度。据我们所知，现有的多线性系统算法还没有复杂度分析。报告的数值结果表明了所提出的 GP 方法的效率。
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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