Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 2: Robinson Stability
In Part 1 of this paper, 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.
KeywordsSmooth parametric optimization problem Smooth functional constraint Stationary point set map Robinson stability Coderivative
Mathematics Subject Classification49K40 49J53 90C31 90C20
This work was supported by National Foundation for Science & Technology Development (Vietnam) and the Grant MOST 105-2115-M-039-002-MY3 (Taiwan). The authors are grateful to the anonymous referees for their careful readings, encouragement, and valuable suggestions. Section 5 is based on the comments made by one of the referees.
- 1.Huyen, D.T.K., Yao, J.-C., Yen, N.D.: Sensitivity analysis of a stationary point set map under total perturbations. Part 1: Lipschitzian stability. J. Optim. Theory Appl. https://doi.org/10.1007/s10957-018-1294-5