In this paper,we mainly focus on the solving approach for the linear trilevel programming(LTP)problem.Firstly,based on the lower-level problem’s Karush–Kuhn–Tucker(K-K-T)optimality conditions,we transform the LTP p...In this paper,we mainly focus on the solving approach for the linear trilevel programming(LTP)problem.Firstly,based on the lower-level problem’s Karush–Kuhn–Tucker(K-K-T)optimality conditions,we transform the LTP problem into a bilevel programming(BP)problem with complementary constraints.Secondly,taking the complementary constraints as penalties and appending them to the upper-level objective,a penalized BP problem is obtained.Thirdly,for the penalized BP problem,we use K-K-T optimality conditions again and append the corresponding complementary conditions to the upper level as penalties.Then,an overall penalized problem for the LTP problem is formed;we analyze the characteristics of the optimal solutions of the overall penalized problem and propose a penalty function algorithm.The numerical results show that the penalty function approach is feasible and effective.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12271061,11771058)the Outstanding Youth Foundation of Hubei Province of China(No.2019CFA088).
文摘In this paper,we mainly focus on the solving approach for the linear trilevel programming(LTP)problem.Firstly,based on the lower-level problem’s Karush–Kuhn–Tucker(K-K-T)optimality conditions,we transform the LTP problem into a bilevel programming(BP)problem with complementary constraints.Secondly,taking the complementary constraints as penalties and appending them to the upper-level objective,a penalized BP problem is obtained.Thirdly,for the penalized BP problem,we use K-K-T optimality conditions again and append the corresponding complementary conditions to the upper level as penalties.Then,an overall penalized problem for the LTP problem is formed;we analyze the characteristics of the optimal solutions of the overall penalized problem and propose a penalty function algorithm.The numerical results show that the penalty function approach is feasible and effective.
