We consider fractional maximization and minimization problems with an arbitrary feasible set, with a convex function in the numerator, and with a concave function in the denominator. These problems have many applications in economics and engineering. It has been shown that both of kind of problems belongs to a class of global optimization problems. These problems can be treated as quasiconvex maximization and minimization problems under certain conditions. For such problems we use the approach developed earlier. The approach based on the special Global Optimality Conditions according to the Global Search Theory proposed by A. S. Strekalovsky. For the case of convex feasible set, we reduce the original minimization problem to pseudoconvex minimization problem showing that any local solution is global. On this basis, two approximate numerical algorithms for fractional maximization and minimization problems are developed. Successful computational experiments have been done on some test problems with a dimension up to 1000 variables.

1. Bector C.R. Duality in Nonlinear Fractional Programming. Zeitschrift fur Operations Research, 1973, no. 17, pp. 183–193.

2. Bertsekas D.P. Nonlinear Programming. Belmont, Athena Scientific, 1999.

3. Dinkelbach W. On Nonlinear Fractional Programming. Management Science, 1978, vol. 13, no. 7, pp. 492–498.

4. Enkhbat R. Quasiconvex Programming and its Applications. Germany, Lambert Publisher, 2009.

5. Hadjisavvas N., Komlosi S., Schaible S. (eds.). Handbook of Generalized Convexity and Generalized Monotonicity. Berlin, Springer, 2005.

6. Horst R., Pardalos P.M., Thoat N.V. Introduction to Global Optimization. Netherlands, Kluwer Academic Publishers, 1995.

7. Katzner D.W. The Walrasion Vision of the Microeconomy. The University of Michigan Press, 1994.

8. Pardalos P.M., Pillips A.T. Global Optimization of Fractional Programs. Journal of Global Optimization, 1991, vol. 1, pp. 173–182.

9. Schaible S. Fractional programming II, On Dinkelbach’s Algorithm. Management Science, 1967, vol. 22, no. 8, pp. 868–873.

10. Strekalovsky A.S. Elements of Nonconvex Optimization (in Russian). Novosibirsk, Nauka, 2003.