This paper presents a practical method for finding the globally optimal solution to nonlinear 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 the problems presented in previous papers on sum-of-ratios problem.
1162,Center of Natural Science, University of Sciences, Pyongyang, DPR Korea, May, 2012