A parametric solution method for a generalized fractional programming problem

This paper proposes a parametric method for solving a generalized fractional programming problem which is called sum-of-ratios problem. The sum-of-ratios problems occur in many fields including computer vision, finance, engineering and management. Compared with other methods based on branch-and-bound procedure, our algorithm is based on Newton-like method for solving a system of nonlinear equations with parameters and it needs to solve convex programming problem in each iteration. We showed the global linear and local superlinear/quadratic rate of convergence of the algorithm. We demonstrated the practical efficiency of the algorithm by numerical experiments for various kinds of sum-of-ratios problem. In the numerical experiments, our method exhibited better solution quality and better convergence rate than other methods.