Approximate Karush-Kuhn-Tucker condition for multi-objective optimistic bilevel programming problems

The approximate Karush-Kuhn-Tucker (AKKT) condition is introduced being a necessary of the local weak efficient solution for optimistic bilevel optimization problems with multiple objectives in upper-level problems. We transform multi-objective problem into single-level by means value function transformation or KKT transformation. then prove that AKKT point to be without any constraint qualification transformed one-level problem. Besides, we give examples show has no lower-level violates Slater CQ, but may have an point, and introduce some suitable qualifications can ensure implies condition. Finally, numerical results are given conditions' necessity.