Uniqueness of KKT multipliers in multiobjective programming

Giancarlo Bigi and Marco Castellani


The uniqueness of the KKT multipliers of a nonlinear program has been studied in a 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 Mangasarian-Fromotivtz type regularity condition, which involves also the objective functions; 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 very recent paper.

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