A relaxation solving approach for the linear trilevel programming problem

In this paper, the global and local optimal solutions of the linear trilevel programming problem are concerned. First, we replace the lower level problem with its optimality conditions, and obtain the bilevel programming problem with the complementary constraints in the inside programming problem. Based on the optimal value function transformation of the inside programming problem, we construct the relaxed problem. Then, we propose the relaxation algorithm, which can approximate the feasible set of the obtained bilevel programming problem successively, and prove the global and local convergence. Numerical results show that the proposed algorithm is feasible and efficient.