Set-valued interpolation, differential inclusions, and sensitivity in optimization

F. Lempio: Set-valued interpolation, differential inclusions, and sensitivity in optimization
in: Recent Developments in Well-Posed Variational Problems, R. Lucchetti, J. Revalski (eds.)
Mathematics and Its Applications 331, Kluwer Academic Publishers, Dordrecht-Boston-London, 1995, 137 - 169

DOI: 10.1007/978-94-015-8472-2_6
MR Nummer: 1351743
Zentralblattnummer: 0868.34011
Keywords: differential inclusions, difference methods, set-valued interpolation, set-valued integration, Aumann's integral, sensitivity in optimization, attainable sets
Mathematics Subject Classification Code: 34A60 (49M25 65D05 65D30 65L05 90C31 93B03)
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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.


1. Introduction
2. Set-Valued Interpolation
3. Representation of the Interpolation Error
4. The Rôle of Sensitivity
5. Set-Valued Integration
6. Approximating Reachable Sets by Set-Valued Integration and Interpolation

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