Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions

摘要

In the present paper, we discuss second-order optimality conditions inconstrained vector optimization problems, where the objective functions andactive constraint functions are locally Lipschitz at the referee point. Byusing the second-order upper generalized directional derivative and thesecond-order tangent set, we introduce a new type of second-order regularitycondition in the sense of Abadie. Then we establish some second-orderKarush-Kuhn-Tucker necessary optimality conditions in primal form for local(weak, Geoffrion properly) efficient solutions to the considered problem.Examples are given to illustrate the obtained results.