A practical but rigorous approach to sum‐of‐ratios optimization in geometric applications

In this paper, we develop an algorithm for minimizing the L q norm of a vector whose components are linear fractional functions, where q is an arbitrary positive integer. The problem is a kind of sum‐of‐ratios optimization problem, and often occurs in computer vision. In that case, it is characterized by a large number of ratios and a small number of variables. The algorithm we propose here exploits this feature and generates a globally optimal solution in a practical amount of computational time.