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In the present paper, we focus on the vector optimization problems withinequality constraints, where objective functions and constrained functions areFr\'echet differentiable, and whose gradient mapping is locally Lipschitz on anopen set. By using the second-order symmetric subdifferential and thesecond-order tangent set, we propose two types of second-order regularityconditions in the sense of Abadie. Then we establish some strong second-orderKarush--Kuhn--Tucker necessary optimality conditions for Geoffrion properlyefficient solutions of the considered problem. Examples are given to illustratethe obtained results.

Strong Second-Order Karush--Kuhn--Tucker Optimality Conditions for Vector Optimization