Coderivatives of a Karush-Kuhn-Tucker point set map and applications. (English) Zbl 1282.90187
Summary: The problem of minimizing a linear-quadratic function over the Euclidean ball is encountered frequently in the theory of trust-region methods in nonlinear programming. By some tools from Variational Analysis, we investigate the stability of the Karush-Kuhn-Tucker point set map of that problem with respect to total perturbations of its data. Verifiable sufficient conditions for the local Lipschitz-like property of the map are obtained, and the connection of our results with the existing criteria for the lower semicontinuity of this Karush-Kuhn-Tucker point set map is shown.
MSC:
| 90C31 | Sensitivity, stability, parametric optimization |
| 49J53 | Set-valued and variational analysis |
| 26B10 | Implicit function theorems, Jacobians, transformations with several variables |
Keywords:
trust-region subproblem; KKT point set map; normal cone; coderivative; local Lipschitz-like propertyReferences:
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