A Penalty Function Method for Solving Nonlinear-Linear Bilevel Programming Problem
非线性-线性二层规划问题的罚函数方法

By using the Kuhn-Tucker optimality condition of the lower level problem, a class of nonlinear bilevel programming problem, whose lower level problem is linear programming problem, is transformed 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. Throughanalyzing the properties of the penalized problem, the optimality condition of the nonlinear bilevel programming problem is given and an algorithm to solve it is proposed. The numerical result shows that the algorithm is feasible and efficient.