Conical Partition Algorithm for Maximizing the Sum of dc Ratios

The following problem is considered in this paper : maxx∈D{∑mj=1 gj(x)/hj(x)}, where gj(x) ≥ 0 and hj(x) > 0, j = 1, · · · , m are d.c. (difference of convex) functions over a convex compact set D in R. Specifically, it is reformulated into the problem of maximizing a linear objective function over a feasible region defined by multiple reverse convex functions. Several favorable properties are developed and a branch-and-bound algorithm based on the conical partition and the outer approximation scheme is presented. Some preliminary results of numerical experiments are reported on the efficiency of the proposed algorithm.