On Second‐Order Optimality Conditions for Vector Optimization

In this article, two second-order constraint qualifications for the vector optimization problem are introduced, that come from first-order constraint qualifications, originally devised for the scalar case. The first is based on the classical feasible arc constraint qualification, proposed by Kuhn and Tucker (1951) together with a slight modification of McCormick’s second-order constraint qualification. The second–the constant rank constraint qualification–was introduced by Janin (1984). They are used to establish two second-order necessary conditions for the vector optimization problem, with general nonlinear constraints, without any convexity assumption.