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

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.

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