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

Practical Global Optimization Algorithm for the Sum-of-Ratios Problem