A penalty function method based on Kuhn–Tucker condition for solving linear bilevel programming

Using the Kuhn–Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty. Then we decompose the linear bilevel programming into a series of linear programming problems and get the optimal solution of the linear bilevel programming using linear programming method.