A primal-dual interior point algorithm for solving bilevel programming problem

Linear bilevel programming problem is a decentralized decision problem with two hierarchical decision units. The rational reaction set of the linear bilevel programming problem is usually nonconvex, hence the problem is classified as a nonlinear optimization problem. This paper presents a modified primal-dual interior point algorithm for solving linear bilevel programming problem. A numerical example is used to illustrate the algorithm. Computational experiments are conducted to test the accuracy and efficiency of the proposed algorithm, and to demonstrate its performance.