On the Global Optimization of Sums of Linear Fractional Functions over a Convex Set

Abstract

The global optimization of the sum of linear fractional functions has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are nonconvex, various specialized algorithms have been proposed for globally solving these problems. However, these algorithms may be difficult to implement and are usually relatively inaccessible. In this article, we show that, by using suitable transformations, a number of potential and known methods for globally solving these problems become available. These methods are often more accessible and use more standard tools than the customized algorithms proposed to date. They include, for example, parametric convex programming and concave minimization methods.