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The paper is published in:
R. Lucchetti and J. Revalski (eds.): Recent Developments in WellPosed Variational Problems,
Dordrecht: Kluwer Academic Publishers, 1995, pp. 137169.
 MSC:
 34A60 Equations with multivalued righthand sides, See Also
 49M25 Finite difference methods
 65D05 Interpolation
 65D30 Numerical integration
 65L05 Initial value problems
 90C31 Sensitivity, stability, parametric optimization
 93B03 Attainable sets
 Keywords:

differential inclusions, difference methods, setvalued interpolation, setvalued integration, Aumanns's integral, sensitivity
in optimization, attainable sets
 Abstract:

Setvalued 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 finitedimensional 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
setvalued mappings.
 Table of Contents:

1. Introduction
2. SetValued Interpolation
3. Representation of the Interpolation Error
4. The Rôle of Sensitivity
5. SetValued Integration
6. Approximating Reachable Sets by SetValued Integration and Interpolation
©
Robert Baier
Last modified: Thu May 28 15:02:47 MDT 1998