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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Vydané v:Journal of optimization theory and applications Ročník 180; číslo 1; s. 91 - 116
Hlavní autori: Huyen, Duong Thi Kim, Yao, Jen-Chih, Yen, Nguyen Dong
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.01.2019
Springer Nature B.V
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ISSN:0022-3239, 1573-2878
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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 ).
AbstractList 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 ).
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).
Author Huyen, Duong Thi Kim
Yao, Jen-Chih
Yen, Nguyen Dong
Author_xml – sequence: 1
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  fullname: Huyen, Duong Thi Kim
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  givenname: Jen-Chih
  surname: Yao
  fullname: Yao, Jen-Chih
  organization: Center for General Education, China Medical University
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  givenname: Nguyen Dong
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  fullname: Yen, Nguyen Dong
  email: ndyen@math.ac.vn
  organization: Institute of Mathematics, Vietnam Academy of Science and Technology
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Issue 1
Keywords 90C31
90C20
Lipschitz-like property
49J53
49K40
Coderivative
Smooth functional constraint
Smooth parametric optimization problem
Stationary point set map
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Snippet 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...
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...
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SubjectTerms 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
Title Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability
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