Global Optimization Algorithms for a Class of Fractional Programming Problems

This paper addresses the problem of minimizing a sum of fractional functions over a convex set, where each fractional function is described by the ratio between a convex and a concave function. Linear-fractional programming problems fall into this category as important special cases. Two global optimization algorithms based on a suitable reformulation of the problem in the outcome space are proposed. Global minimizers are obtained as the limit of the optimal solutions of a sequence of special indefinite quadratic programs, solved by using a constraint enumeration procedure, according with the first algorithm, and a sequence of special linear-fractional programs, solved by using a rectangular branch and bound procedure, according to the second. Both algorithms exploit the relatively small number of half-spaces needed for approximating the original problem in the outcome space. A comparison of the algorithms based on some computational experiences is reported.