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A result on sets, with applications to vector optimization

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Abstract

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.

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References

  1. Fuchssteiner B, König H (1980) New versions of the Hahn-Banach theorem. In: Beckenbach EF (ed) General Inequalities. Birkhäuser Verlag, Basel, pp 255–266

    Google Scholar 

  2. Holmes RB (1975) Geometrical Functional Analysis and its Applications. Springer, New York

    Google Scholar 

  3. Martellotti A, Salvadori A (1988) A minimax theorem for functions taking values in a Riesz space. J Math Anal Appl 133:1–13

    Google Scholar 

  4. Oettli W (1984) On a new version of the Hahn-Banach theorem. In: Cottle RW et al. (eds) Mathematical Programming. North Holland, Amsterdam New York Oxford, pp 289–295

    Google Scholar 

  5. Penot JP, Thera M (1982) Semi-continuous mappings in general topology. Arch Math 38:158–166

    Google Scholar 

  6. Peressini A (1967) Ordered Topological Vector Spaces. Harper & Row, New York

    Google Scholar 

  7. Zălinescu C (1983) Duality for vectorial nonconvex optimization by convexification and applications. An St. Univ. Al I Cuza Iaşi, s I a Mat 29(3):15–34

    Google Scholar 

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Authors and Affiliations

  1. Factulty of Mathematics, University of Iasi, 6600, Iasi, Romania

    C. Zălinescu

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  1. C. Zălinescu
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Zălinescu, C. A result on sets, with applications to vector optimization. ZOR - Methods and Models of Operations Research 35, 291–298 (1991). https://doi.org/10.1007/BF01417517

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  • DOI: https://doi.org/10.1007/BF01417517

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