On Abadie constraint qualification for multiobjective optimization problems

Abstract

We state the Abadie constraint qualification for multiobjective optimization problems involving inequality, equality constraints and a closed abstract set constraint and derive the necessary optimality conditions at weak Pareto optimal solutions based on the limiting subdifferential. In contrast to the most developed works on multiobjective problems, this constraint qualification entirely depends on the feasible set. Moreover, the relationship between the Abadie constraint qualification and the local error bound condition is studied. Finally some examples are provided to clarify our results. © 2017, Springer-Verlag Italia S.r.l., part of Springer Nature.