Necessary Optimality Conditions for Multiobjective Bilevel Programs

The multiobjective bilevel program is a sequence of two optimization problems, with the upper‐level problem being multiobjective and the constraint region of the upper level problem being determined implicitly by the solution set to the lower‐level problem. In the case where the Karush‐Kuhn‐Tucker (KKT) condition is necessary and sufficient for global optimality of all lower‐level problems near the optimal solution, we present various optimality conditions by replacing the lower‐level problem with its KKT conditions. For the general multiobjective bilevel problem, we derive necessary optimality conditions by considering a combined problem, with both the value function and the KKT condition of the lower‐level problem involved in the constraints. Most results of this paper are new, even for the case of a single‐objective bilevel program, the case of a mathematical program with complementarity constraints, and the case of a multiobjective optimization problem.