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.
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