On Approximate Efficiency in Multiobjective Programming

This paper is focused on approximate ( $$\varepsilon$$ -efficient) solutions of multiobjective mathematical programs. We introduce a new $$\varepsilon$$ -efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these $$\varepsilon$$ -efficient solutions in convex multiobjective programs through approximate solutions of linear scalarizations, which allow us to obtain parametric representations of different $$\varepsilon$$ -efficiency sets. Several classical $$\varepsilon$$ -efficiency notions are considered in order to show the concepts introduced and the results obtained. Copyright Springer-Verlag 2006