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.
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This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.
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Gutiérrez, C., Jiménez, B. & Novo, V. On Approximate Efficiency in Multiobjective Programming. Math Meth Oper Res 64, 165–185 (2006). https://doi.org/10.1007/s00186-006-0078-0
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DOI: https://doi.org/10.1007/s00186-006-0078-0
Keywords
- Multiobjective mathematical programming
- \(\varepsilon\)-efficiency
- Scalarization
- Weighting method
- Parametric representation