Improved equilibrium point algorithm of linear bilevel programming

In this paper, an algorithm for finding an ε-globally optimal solution of the linear bilevel programming problem (LBP) is considered. We call this algorithm the improved equilibrium point algorithm. It is based on the notion of the basic equilibrium point algorithm. We propose the algorithm by adding a new cutting plan in the constraint conditions, and combining with the bilinear programming problem. Compared with the basic equilibrium point algorithm, the calculation burden is reduced when the improved equilibrium point algorithm is used in solving the LBP. At last a numerical example is given to illustrate how the algorithm works.