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Semiconvergence in distribution of random closed sets with application to random optimization problems

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  • Silvia Vogel

Abstract

The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence statements for suitable functions of random sets are proved and the results are employed to derive stability statements for random optimization problems where the objective function and the constraint set are approximated simultaneously. Copyright Springer Science + Business Media, Inc. 2006

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  • Silvia Vogel, 2006. "Semiconvergence in distribution of random closed sets with application to random optimization problems," Annals of Operations Research, Springer, vol. 142(1), pages 269-282, February.
    • Handle: RePEc:spr:annopr:v:142:y:2006:i:1:p:269-282:10.1007/s10479-006-6172-0
    DOI: 10.1007/s10479-006-6172-0
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    References listed on IDEAS

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    1. Alan J. King & R. Tyrrell Rockafellar, 1993. "Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 148-162, February.
    2. Alan J. King, 1989. "Generalized Delta Theorems for Multivalued Mappings and Measurable Selections," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 720-736, November.
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