Sensitivity Analysis in Parametric Convex Vector Optimization

In this paper, sensitivity analysis of the efficient sets in parametric convex vector optimization is considered. Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps. We establish the formulas for computing the Fréchet coderivative of the profile...

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Vydáno v:Set-valued and variational analysis Ročník 32; číslo 4; s. 29
Hlavní autoři: An, Duong Thi Viet, Tung, Le Thanh
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.12.2024
Springer Nature B.V
Témata:
Analysis
Approximation
Convex analysis
Convexity
Mathematics
Mathematics and Statistics
Optimization
Parameter sensitivity
Perturbation
Sensitivity analysis
90C31
Sensitivity analysis
49K40
49J52
90C25
Fréchet coderivative
Perturbation map
90C29
Parametric convex vector optimization
Weak perturbation map
Proper perturbation map
Domination property
ISSN:1877-0533, 1877-0541
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Shrnutí:In this paper, sensitivity analysis of the efficient sets in parametric convex vector optimization is considered. Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps. We establish the formulas for computing the Fréchet coderivative of the profile of the above three kinds of perturbation maps. Because of the convexity assumptions, the conditions set are fairly simple if compared to those in the general case. In addition, our conditions are stated directly on the data of the problem. It is worth emphasizing that our approach is based on convex analysis tools which are different from those in the general case.
Bibliografie:ObjectType-Article-1
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-024-00733-3