In G. Haeser, A. Ramos, Constraint Qualifications for Karush-Kuhn-Tucker Conditions in Multiobjective Optimization, JOTA, Vol.~187 (2020), 469-487, a generalization of the normal cone from single objective to multiobjective optimization is introduced, along with a weakest constraint qualification such that any local weak Pareto optimal point is a weak Kuhn-Tucker point. We extend this approach to other generalizations of the normal cone and corresponding weakest constraint qualifications, such that local Pareto optimal points are weak Kuhn-Tucker points, local proper Pareto optimal points are weak and proper Kuhn-Tucker points, respectively, and strict local Pareto optimal points of order one are weak, proper and strong Kuhn-Tucker points, respectively. The constructions are based on an appropriate generalization of polarity to pairs of matrices and vectors.
Citation
Optimization Online, 2022