The Bounds of Solutions to Polynomial Complementarity Problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-23 DOI:10.1007/s10957-024-02511-5

Xue-liu Li, Guo-ji Tang

引用次数: 0

Abstract

The polynomial complementarity problem (PCP) is an important extension of the tensor complementarity problem (TCP). The main purpose of the present paper is to extend the results on the bounds of solutions of TCP due to Xu–Gu–Huang from TCP to PCP. To that end, the concepts of (generalized) row strictly diagonally dominant tensor to tensor tuple are extended and the properties about them are discussed. By using the introduced structured tensor tuples, the upper and lower bounds on the norm of solutions to PCP are derived. Comparisons between the results presented in the present paper and the existing bounds are made.

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多项式互补问题解的边界

多项式互补问题（PCP）是张量互补问题（TCP）的重要扩展。本文的主要目的是将徐谷黄关于 TCP 解的边界的结果从 TCP 扩展到 PCP。为此，本文扩展了（广义）行严格对角显性张量到张量元组的概念，并讨论了它们的相关性质。通过使用引入的结构张量元组，推导出了 PCP 解的规范上界和下界。本文提出的结果与现有的界限进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.