Given symmetric matrices B,D ∈ R n×n and a symmetric positive definite
matrix W ∈ R n×n , maximizingthe sum of the Rayleighquotientx ? Dx andthe gener-
alized Rayleigh quotient
x ? Bx
x ? Wx
on the unit sphere not only is of mathematical interest
in
This paper presents a practical method for nding the globally optimal solution
to nonlinear sum-of-ratios problem arising in image processing, engineering and man-
agement. Unlike traditional methods which may get trapped in local minima due
to th
