We show that efficient points can be obtained with the weighted norm scalarization under assumptions less restrictive than in the existing literature. For properly efficient points with a given trade-off bound, we provide an easy-to-compute lower bound on the norm parameter that allows the approximation of the desired points
within a specified tolerance. We apply a technique from machine learning that allows for stable computations, even for larger values of the norm parameter,
and solve some test instances of the weighted norm scalarization globally with the alpha-BB method.