On Approximate Efficiency in Multiobjective Programming

C. Gutiérrez (), B. Jiménez () and V. Novo ()

Mathematical Methods of Operations Research, 2006, vol. 64, issue 1, 165-185

Abstract: 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

Keywords: Multiobjective mathematical programming; $$\varepsilon$$ -efficiency; Scalarization; Weighting method; Parametric representation; 49J52; 90C29; 49M37 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (15)

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DOI: 10.1007/s00186-006-0078-0

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