An efficient global optimization algorithm for maximizing the sum of two generalized Rayleigh quotients

@article{Wang2017AnEG,
  title={An efficient global optimization algorithm for maximizing the sum of two generalized Rayleigh quotients},
  author={Xiaohui Wang and Longfei Wang and Yong Xia},
  journal={Computational and Applied Mathematics},
  year={2017},
  volume={37},
  pages={4412-4422}
}
Maximizing the sum of two generalized Rayleigh quotients (SRQ) can be reformulated as a one-dimensional optimization problem, where the function value evaluations are reduced to solving semi-definite programming (SDP) subproblems. In this paper, we first use the dual SDP subproblem to construct an explicit overestimation and then propose a branch-and-bound algorithm to globally solve (SRQ). Numerical results demonstrate that it is even more efficient than the recent SDP-based heuristic… 

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