Second-order Karush-Kuhn-Tucker necessary conditions in locally Lipschitz vector optimization with inequality constraints
Nguyễn Văn Tuyên, Jen‐Chih Yao, Ching‐Feng Wen · arXiv (Cornell University) · 2017
In the present paper, we discuss second-order optimality conditions in constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. By using the second-order upper generalized directional derivative and the second-order tangent set, we introduce a new type of second-order regularity condition in the sense of Abadie. Then we establish some second-order Karush-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.