Title: An efficient global optimization algorithm for maximizing the sum of two generalized Rayleigh quotients,
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.