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Set-Valued Interpolation, Differential Inclusions, and Sensitivity in Optimization

  • F. Lempio
Part of the Mathematics and Its Applications book series (MAIA, volume 331)

Abstract

Set-valued interpolation and integration methods are introduced with special emphasis on error representations and error estimates with respect to Hausdorff distance. The connection between order of convergence results and sensitivity properties of finite-dimensional convex optimization problems is discussed. The results are applied to the numerical approximation of reachable sets of linear control problems by quadrature formulae and interpolation techniques for set-valued mappings.

(AMS) Subject Classification

34A60 49M25 65D05 65D30 65L05 90C31 93B03 

Keywords

differential inclusions difference methods set-valued interpolation set-valued integration Aumanns’s integral sensitivity in optimization attainable sets 

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • F. Lempio
    • 1
  1. 1.Lehrstuhl für Angewandte MathematikUniversität BayreuthBayreuthFederal Republic of Germany

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