Boundedness and Uniqueness of Lagrange Multipliers for Multiobjective Optimization Problems with Vanishing Constraints
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Abstract
In this paper, we study a multiobjective optimization problem with vanishing constraints. Here, we introduce proper M- and S-regularity conditions, which provide the necessary and sufficient conditions for nonemptiness and boundedness of some sets of Lagrange multipliers. Further, we investigate the uniqueness of the Lagrange multipliers by introducing the concept of strict-Mangasarian Fromovitz constraint qualification for the multiobjective optimization problem with vanishing constraints. We show that this strict constraint qualification is equivalent to the uniqueness of the Lagrange multipliers.
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