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Frank Lempio

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

The paper is published in:
R. Lucchetti and J. Revalski (eds.): Recent Developments in Well-Posed Variational Problems,
Dordrecht: Kluwer Academic Publishers, 1995, pp. 137-169.

34A60 Equations with multivalued right-hand sides, See Also
49M25 Finite difference methods
65D05 Interpolation
65D30 Numerical integration
65L05 Initial value problems
90C31 Sensitivity, stability, parametric optimization
93B03 Attainable sets

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

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.

Table of Contents:
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

© Robert Baier
Last modified: Thu May 28 15:02:47 MDT 1998