On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere

@article{Zhang2013OnOT,
  title={On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere},
  author={Lei-Hong Zhang},
  journal={Comp. Opt. and Appl.},
  year={2013},
  volume={54},
  pages={111-139}
}
Given symmetric matrices B,D ∈ Rn×n and a symmetric positive definite matrix W ∈ Rn×n, maximizing the sum of the Rayleigh quotient x>Dx and the generalized Rayleigh quotient x >Bx x>Wx on the unit sphere not only is of mathematical interest in its own right, but also finds applications in practice. In this paper, we first present a real world application arising from the sparse Fisher discriminant analysis. To tackle this problem, our first effort is to characterize the local and global maxima… CONTINUE READING

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