The basic properties and algorithm of a linear bilevel programming model with multiple followers

The geometric properties and optimality conditions for a class of typical model of linear bilevel programming with multiple followers are discussed in this paper. Under the assumption that the constrained set is nonempty and bounded, we study the geometric properties of the feasible set and reach the conclusion of the feasible set of weak quasi-convex and connected set. An optimum condition is obtained by using the duality theory of linear programming. According to these properties, an algorithm is proposed to solve the model and to verify the correctness of the theory and the feasibility of algorithm by giving the examples of numerical calculation.