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

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Abstract

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 algorithm.

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Acknowledgements

The authors are grateful to the two anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Astronautics, Beihang University, Beijing, 100191, People’s Republic of China

    Xiaohui Wang

  2. LMIB of the Ministry of Education, School of Mathematics and System Sciences, Beihang University, Beijing, 100191, People’s Republic of China

    Longfei Wang & Yong Xia

Authors
  1. Xiaohui Wang
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  2. Longfei Wang
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  3. Yong Xia
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Corresponding author

Correspondence to Yong Xia.

Additional information

Communicated by Ernesto G. Birgin.

This research was supported by NSFC under Grants 11571029, 11471325 and 11771056, and by fundamental research funds for the Central Universities under Grant YWF-17-BJ-Y-52.

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Wang, X., Wang, L. & Xia, Y. An efficient global optimization algorithm for maximizing the sum of two generalized Rayleigh quotients. Comp. Appl. Math. 37, 4412–4422 (2018). https://doi.org/10.1007/s40314-018-0575-9

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  • DOI: https://doi.org/10.1007/s40314-018-0575-9

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