A Strict Constraint Qualification in Vector Optimization

The main aim of this paper is to present the notion of cone-continuity property introduced by Andreani et al. (Andreani, R., Martínez, J.M., Ramos, A. and Silva, P.J.S., A cone-continuity constraint qualification and algorithmic consequences, SIAM J. Optim., 26(2016), 96–110) in the context of vector optimization. We extend this property and establish it to be a strict regularity condition while dealing with efficient solutions. This property is the weakest condition which ensures that weak approximate Karush-Kuhn-Tucker conditions imply weak Karush-Kuhn-Tucker conditions. Further, cone-continuity is established to be a strict constraint qualification while dealing with weak and proper efficient solutions.