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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 180; no. 1; pp. 117 - 139
Main Authors: Huyen, Duong Thi Kim, Yao, Jen-Chih, Yen, Nguyen Dong
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2019
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Sensitivity analysis
Stability
Theory of Computation
Robinson stability
90C31
90C20
49J53
49K40
Coderivative
Smooth functional constraint
Smooth parametric optimization problem
Stationary point set map
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1295-4