Global Minimization for Generalized Polynomial Fractional Program

This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional programproblem (P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. Theproposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonicoptimization problem of (P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigatedregion in which the global optimal solution of (P) does not exist, which can be seen as an accelerating device for the solution algorithm of (P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing thealgorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach forsolving problem (P) provided that the number of variables is not too large