The finite criss-cross method for hyperbolic programming

In this paper the finite criss-cross method is generalized to solve hyperbolic (fractional linear) programming problems. Just as in the case of linear or quadratic programming the criss-cross method can be initialized with any, not necessarily feasible basic solution. It is known that if the feasible region of the problem is unbounded then some of the known algorithms fail to solve the problem. Our criss-cross algorithm does not have such drawback. Finiteness of the procedure is proved under the usual mild assumptions. Some small numerical examples illustrate the main features of the algorithm and show that our method generates different iterates than other earlier published methods.