Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 2: Robinson Stability

Duong Thi Kim Huyen (), Jen-Chih Yao () and Nguyen Dong Yen ()
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Duong Thi Kim Huyen: Vietnam Academy of Science and Technology
Jen-Chih Yao: China Medical University
Nguyen Dong Yen: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 1, No 8, 117-139

Abstract: Abstract 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.

Keywords: Smooth parametric optimization problem; Smooth functional constraint; Stationary point set map; Robinson stability; Coderivative; 49K40; 49J53; 90C31; 90C20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1295-4

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