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Characterization of the equality of weak efficiency and efficiency on convex free disposal hulls

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.