  In solving a multi-objective optimization problem by scalarization
techniques, solutions to a scalarized problem are, in general, weakly efficient
rather than efficient to the original problem. Thus, it is crucial to
understand what problem ensures that all weakly efficient solutions are
efficient. In this paper, we give a characterization of the equality of the
weakly efficient set and the efficient set, provided that the free disposal
hull of the domain is convex. By using this characterization, we obtain various
mathematical applications. As a practical application, we show that all weakly
efficient solutions to a multi-objective LASSO with mild modification are
efficient.
