Sensitivity analysis of a stationary point set map under total perturbations. II: Robinson stability. (English) Zbl 1409.49025
Summary: In Part I of our paper [ibid. 180, No. 1, 91–116 (2019; Zbl 1409.49024)], we have estimated the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total perturbations. From these estimates, necessary and sufficient conditions for the local Lipschitz-like property of the map have been obtained. In this part, we establish sufficient conditions for the Robinson stability of the stationary point set map. This allows us to revisit and extend several stability theorems in indefinite quadratic programming. A comparison of our results with the ones which can be obtained via another approach is also given.
MSC:
| 49K40 | Sensitivity, stability, well-posedness |
| 49J53 | Set-valued and variational analysis |
| 90C31 | Sensitivity, stability, parametric optimization |
| 90C20 | Quadratic programming |
Keywords:
smooth parametric optimization problem; smooth functional constraint; stationary point set map; Robinson stability; Fréchet coderivative; Mordukhovich coderivativeCitations:
Zbl 1409.49024References:
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