在 Stiefel 流形上最大化两个广义二次矩阵形式函数之比的全局性研究

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-13 DOI:10.1007/s11075-024-01939-0

Longfei Wang, Yu Chen, Hongwei Jiao, Yunhai Xiao, Meijia Yang

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引用次数: 0

摘要

我们考虑的问题是最大化斯蒂费尔流形上两个广义二次矩阵形式函数的比值，即（\max \limits _{X^{T}X=I}\(RQMP).我们利用 Dinkelbach 算法对 RQMP 进行全局求解，其中每个子问题都由闭式解进行评估。对于 RQMP 的一个特例（AB=BA/），我们提出了一个等效的线性规划问题。数值实验证明，它比最近基于 SDP 的算法更有效。

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Globally maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold

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Globally maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold

We consider the problem of maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold, i.e., \(\max \limits _{X^{T}X=I} \frac{\text {tr}(GX^{T}AX)}{\text {tr}(GX^{T}BX)}\) (RQMP). We utilize the Dinkelbach algorithm to globally solve RQMP, where each subproblem is evaluated by the closed-form solution. For a special case of RQMP with \(AB=BA\), we propose an equivalent linear programming problem. Numerical experiments demonstrate that it is more efficient than the recent SDP-based algorithm.

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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.