Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability

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 unde...

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Vydáno v:Journal of optimization theory and applications Ročník 180; číslo 1; s. 91 - 116
Hlavní autoři: Huyen, Duong Thi Kim, Yao, Jen-Chih, Yen, Nguyen Dong
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.01.2019
Springer Nature B.V
Témata:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Sensitivity analysis
Theory of Computation
90C31
90C20
Lipschitz-like property
49J53
49K40
Coderivative
Smooth functional constraint
Smooth parametric optimization problem
Stationary point set map
ISSN:0022-3239, 1573-2878
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Popis
Shrnutí: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 ).
Bibliografie:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1294-5