Vector optimization: Singularities, regularizations

We discuss three scalarizations of the multiobjective optimization from the point of view of the parametric optimization. We analyze three important aspects: i) What kind of singularities may appear in the different parametrizations, ii) Regularizations in the sense of Jongen, Jonker and Twilt, and in the sense of Kojima and Hirabayashi, iii) The Mangasarian–Fromovitz Constraint Qualification for the first parametrization.