Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives

In the paper, we develop some calculus of Studniarski derivatives for set-valued maps. Then, we establish relationships between Studniarski derivatives of a given objective map and that of the weak perturbation map. Finally, applications to sensitivity analysis of a constrained set-valued optimizati...

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Bibliographic Details
Published inPositivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 21; no. 1; pp. 255 - 272
Main Author Anh, Nguyen Le Hoang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2017
Springer Nature B.V
Subjects
Calculus
Calculus of Variations and Optimal Control; Optimization
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Optimization
Potential Theory
Sensitivity analysis
Studies
System theory
Directional metric subregularity
90C31
Calculus rules
Sensitivity analysis
49J53
Set-valued optimization
49J52
Weak perturbation map
Studniarski detivative
54C60
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Summary:In the paper, we develop some calculus of Studniarski derivatives for set-valued maps. Then, we establish relationships between Studniarski derivatives of a given objective map and that of the weak perturbation map. Finally, applications to sensitivity analysis of a constrained set-valued optimization problem are obtained. Several examples are given to illustrate some advantages of our results over recent existing ones in the literature.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-016-0418-0