Multi-table Pivoting Algorithms for Solving Linear Bilevel Programming Problems

Multi-table Pivoting Algorithms is a method Based on pivoting algorithms for solving bi-level linear programming (BLP) problems, however, it is different from previous approaches such as Kuhn-Tucker approach, comlementarity pivot approach in that there is no need for you to add any slack, surplus or artificial variables. In addition, by combination of tables, the method can also solve similar problems such as Linear multilevel programming and linear bilevel multi-follower programming with dependent followers (Stackelberg-Nash equilibrium), and so on. The algorithm´s idea is to make use of pivoting operation table instead of Kuhn-Tucker optimality condition of lower level problem. Finally, an example of linear bi-level programming problem shows that the method can reach its local optimal point quickly and obtain global optimal solution.