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Differential stability of solutions to parametric optimization problems. (English) Zbl 0749.90077
Summary: A method for the differential stability of solutions to a class of parametric optimization problems is proposed. Any solution of the parametric optimization problem is given as a fixed point of the metric projection onto the set of admissible coefficients. A new result on the differential stability of the metric projection in Sobolev space \(H^ 2(\Omega)\) onto a set of admissible parameters is obtained. The stability results with respect to perturbations of observations for the solutions to a coefficient estimation problem for a second-order elliptic equation are derived.

90C31 Sensitivity, stability, parametric optimization
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