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Stability of perturbed optimization problems with applications to parameter estimation. (English) Zbl 0736.49017

A result on Hölder-stability of solutions for optimization problems in Banach spaces is derived; here stability is obtained with respect to a weaker seminorm. The result is applied to parameter estimation problems for elliptic equations. Here, frequently, stability with respect to errors in the observation can only be achieved for a regularized problem. The relation between the original problem and the perturbed and regularized problem is clarified.
Reviewer: F.Colonius

MSC:

49K40 Sensitivity, stability, well-posedness
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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