Necessary optimality condition for trilevel optimization problem
Gaoxi Li, Zhongping Wan, Jiawei Chen, Xiaoke Zhao · Journal of Industrial and Management Optimization · 2018
This paper mainly studies the optimality conditions for a class of trilevel optimization problem, of which all levels are nonlinear programs. We firstly transform this problem into an auxiliary bilevel optimization problem by applying KKT approach to the lower-level problem. Then we obtain a necessary optimality condition via the differential calculus of Mordukhovich. Finally, a theorem for existence of optimal solution is derived via Weierstrass Theorem.