In this paper we propose an optimal method for solving the linear bilevel programming problem with no upper-level constraint.The main idea of this method is that the initial point which is in the feasible region goes forward along the optimal direction firstly.When the iterative point reaches the boundary of the feasible region,it can continue to go forward along the suboptimal direction.The iteration is terminated until the iterative point cannot go forward along the suboptimal direction and effective direction,and the new iterative point is the solution of the lower-level programming.An algorithm which bases on the main idea above is presented and the solution obtained via this algorithm is proved to be optimal solution to the bilevel programming problem.This optimal method is effective for solving the linear bilevel programming problem.
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