The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty fu...The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to l^nd an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at function without lower level problems is defined and lower level problems, a quadratic objective penalty is proved equal to the original bilevel programming.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11271329 and 10971193
文摘The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to l^nd an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at function without lower level problems is defined and lower level problems, a quadratic objective penalty is proved equal to the original bilevel programming.