In this paper, we present an outer approximation algorithm for solving the following problem: maxx∈S{f(x)/g(x)}, where f(x) ⩾ 0 and g(x) > 0 are d.c. (difference of convex) functions over a convex compact subset S of ℝn. Let π(λ) = maxx∈S(f(x) – λg(x)), then the problem is equivalent to finding out a solution of the equation π(λ) = 0. Though the monotonicity of π(λ) is well known, it is very time-consuming to solve the previous equation, because that maximizing (f(x) – λg(x)) is very hard due to that maximizing a convex function over a convex set is NP-hard. To avoid such tactics, we give a transformation under which both the objective and the feasible region turn out to be d.c. After discussing some properties, we propose a global optimization approach to find an optimal solution for the encountered problem.
