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Set-convergence of convex sets and stability in vector optimization

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  • Miglierina Enrico

    (Department of Economics, University of Insubria, Italy)

Abstract

This work establishes the lower convergence of the set of minimal points of An to the set of minimal points of A, whenever An is a sequence of convex subsets of an euclidean space satisfying the dominance property and converging to A. Using this result and introducing a property for a function f that guarantees the convergence of the image f(An) to f(A) when An converges to A, we obtain some stability results in the decision space for a class of suitable perturbations of the feasible region of a vector optimization problem.

Suggested Citation

  • Miglierina Enrico, 2002. "Set-convergence of convex sets and stability in vector optimization," Economics and Quantitative Methods qf0220, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0220
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2002_37.pdf
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    References listed on IDEAS

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    1. X. D. H. Truong, 2001. "Existence and Density Results for Proper Efficiency in Cone Compact Sets," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 173-194, October.
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