Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian 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 7, 116 pages

Abstract: Abstract By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327, 2004) and other related results, we estimate 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 the obtained formulas, we derive necessary and sufficient conditions for the local Lipschitz-like property of the stationary point set map. This leads us to new insights into the preceding deep investigations of Levy and Mordukhovich in the above-cited paper and of Qui (J Optim Theory Appl 161:398–429, 2014, J Glob Optim 65:615–635, 2016).

Keywords: Smooth parametric optimization problem; Smooth functional constraint; Stationary point set map; Lipschitz-like property; 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/s10957-018-1294-5

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