本文探讨了广义瑞利商之和的最大值求解方法，分析了相关数学性质，并提出了一种有效的优化算法。
The Rayleigh quotient is crucial for determining the eigenvalues of symmetric matrices. Additionally, maximizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient over the unit sphere has practical applications in various fields. This maximization problem can occur in the downlink phase of a multi-user MIMO system and in sparse Fisher discriminant analysis within pattern recognition. The calculation of matrix eigenvalues is relevant to numerous problems in engineering and physical sciences. Indeed, eigenspace computation plays a role in multiple areas including control theory, signal processing, structural dynamics, and data mining.
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