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On Approximate Efficiency in Multiobjective Programming

Authors:	C Gutiérrez B Jiménez V Novo

Institution:	(1) Departamento de Matemática Aplicada, E.T.S.I. Informática, Universidad de Valladolid, Edificio de Tecnologías de la Información y las Telecomunicaciones, Campus Miguel Delibes, s/n, 47011 Valladolid, Spain;(2) Departamento de Matemática Aplicada, E.T.S.I. Industriales, UNED, c/ Juan del Rosal, 12, Ciudad Universitaria, 28040 Madrid, Spain

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.This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.

Keywords:	Multiobjective mathematical programming $\varepsilon$ -efficiency" target="_blank">gif" alt="$$\varepsilon$$" align="middle" border="0">-efficiency Scalarization Weighting method Parametric representation
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