Longfei Wang, Yu Chen, Hongwei Jiao, Yunhai Xiao, Meijia Yang
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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.
期刊介绍:
The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.