In this paper we develop and derive the computational cost of an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\varepsilon}$$</EquationSource> </InlineEquation> -approximation algorithm for a class of global optimization problems, where a suitably defined composition of some ratio functions is minimized over a convex set. The result extends a previous one about a class...</equationsource></inlineequation>