Uniqueness of KKT Multipliers in Multiobjective Optimization

The uniqueness of the KKT multipliers of a nonlinear program has been studied ina well-known paper by Kyparisis. In the first part of this note, we show that the characterization obtained in that paper does not provide a satisfactory result for the multiobjective case. Thus, we introduce a new regularity condition, which involves also the objective functions, and we show that it is necessary and sufficient in order to have unique KKT multipliers. Moreover, we use this condition to refine a second-order necessary optimality condition, which has been obtained in a recent paper.