Uniqueness of KKT multipliers in multiobjective programming
Giancarlo Bigi and Marco Castellani
Summary
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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