  This paper presents a practical method for finding the globally optimal
solution to the sum-of-ratios problem arising in image processing, engineering
and management. Unlike traditional methods which may get trapped in local
minima due to the non-convex nature of this problem, our approach provides a
theoretical guarantee of global optimality. Our algorithm is based on solving a
sequence of convex programming problems and has global linear and local
superlinear/quadratic rate of convergence. The practical efficiency of the
algorithm is demonstrated by numerical experiments for synthetic data.
