高阶张量协正性研究的最新进展  

Recent progress on the study of copositivity of high-order tensors

作　　者：陈海滨 CHEN Haibin(School of Management,Qufu Normal University,276826,Rizhao,Shandong,PRC)

机构地区：[1]曲阜师范大学管理学院,山东省日照市276826

出　　处：《曲阜师范大学学报（自然科学版）》2024年第2期46-56,共11页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(12071249);山东省自然科学基金杰出青年基金(ZR2021JQ01)。

摘　　要：大数据时代,承载高阶高维信息的张量结构备受关注,从而引发了关于张量的理论、计算和应用的广泛研究.协正张量作为一种特殊的结构张量,也在材料物理及超图谱理论、多项式优化、张量互补与张量特征值互补等问题中凸显出不可或缺的作用.该文旨在对高阶协正张量数值判定、算法及应用的进展情况进行简单的梳理与总结,并希望对大规模高阶协正张量相关问题的未来发展提供可能的研究方向.In the era of big data,tensors have attracted much attention due to its ability in bearing higher-order and higher-dimensional information,which leads to extensive research on the theory,calculation and application of tensors.As a special structured tensor,the copositive tensor plays an indispensable role in material physics,hypergraph theory,polynomial optimization,tensor complementarity and tensor eigenvalue complementarity.This paper sorts out and summarizes the progress of numerical verification,algorithm and application of high order copositive tensors,and offers potential research avenues for the advancement of large-scale,high-order copositive tensor-related problems in future studies.

关 键 词：协正张量 齐次多项式 张量互补 张量特征值 

分 类 号：O221.2[理学—运筹学与控制论]