Minimization of the ratio of functions defined as sums of the absolute values

This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization. This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time.