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Convergence of the minimal sets under convexity in vector optimization

Author

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  • Miglierina Enrico

    (Department of Economics, University of Insubria, Italy)

  • Molho Elena

    (University of Pavia, Italy)

Abstract

We study the behaviour of the minimal sets of a sequence of convex sets An converging to a given set A. Under suitable assumptions involving only the structure of the single sets An, we obtain the lower convergence of MinAn to MinA. In a reflexive Banach space ordered by a closed convex cone with a weakly compact base, we consider a sequence of convex sets An Mosco-converging to a set A. In the more general setting of a normed linear space ordered by a closed convex based cone (without any assumptions on the compactness of the base), we consider the stronger notion of Attouch-Wets convergence of the sequence of convex sets An. We compare our theorems with existing results related to the same topic.

Suggested Citation

  • Miglierina Enrico & Molho Elena, 2003. "Convergence of the minimal sets under convexity in vector optimization," Economics and Quantitative Methods qf0302, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0302
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2003_2.pdf
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    References listed on IDEAS

    as
    1. E. Miglierina & E. Molho, 2002. "Scalarization and Stability in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 657-670, September.
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