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

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

引用次数: 0

Abstract

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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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

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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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

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