On Approximate Efficiency in Multiobjective Programming
This paper is focused on approximate ( <InlineEquation ID="IEq19"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation>-efficient) solutions of multiobjective mathematical programs. We introduce a new <InlineEquation ID="IEq20"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation>-efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these <InlineEquation ID="IEq21"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation>-efficient solutions in convex multiobjective programs through approximate solutions of linear scalarizations, which allow us to obtain parametric representations of different <InlineEquation ID="IEq22"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation>-efficiency sets. Several classical <InlineEquation ID="IEq23"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation>-efficiency notions are considered in order to show the concepts introduced and the results obtained. Copyright Springer-Verlag 2006
