Global Optimization of Nonlinear Sums of Ratios

The nonlinear sum of ratios problem (P) has several important applications. However, it is also a difficult problem to solve, since it generally possesses many local optima that are not global optima. In this article we present and show the convergence of an algorithm for finding a global optimal solution to problem (P). The algorithm uses a branch and bound search procedure that globally solves problem (P) by concentrating primarily on solving an equivalent outcome space version of the problem. The algorithm can be implemented by using standard convex programming methods.