Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional single level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modified convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.