Optimality conditions for pessimistic trilevel optimization problem with middle-level problem being pessimistic

This paper mainly studies the optimality conditions for a class of pessimistic trilevel optimization problem, of which middle-level is a pessimistic problem. We firstly translate this problem into an auxiliary pessimistic bilevel optimization problem, by applying KKT approach for the lower level problem. Then we obtain a necessary optimality condition via the differential calculus of Mordukhovich. Finally, we obtain an existence theorem of optimal solution by direct method.