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

Journal Article · Sat Sep 15 00:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-018-0575-9· OSTI ID:22769238

Wang, Xiaohui ^[1]; Wang, Longfei; Xia, Yong ^[2]

---

1. Beihang University, School of Astronautics (China)
2. Beihang University, LMIB of the Ministry of Education, School of Mathematics and System Sciences (China)

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.

• OSTI ID: 22769238
• Journal Information: Computational and Applied Mathematics, Vol. 37, Issue 4; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
ONE-DIMENSIONAL CALCULATIONS
OPTIMIZATION
PROGRAMMING