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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Bibliographic Details
Published in:Set-valued and variational analysis 2024-12, Vol.32 (4), Article 29
Main Authors: An, Duong Thi Viet, Tung, Le Thanh
Format: Article
Language:English
Subjects:
Analysis
Convexity
Mathematics
Mathematics and Statistics
Optimization
Parameter sensitivity
Perturbation
Sensitivity analysis
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Summary: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.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-024-00733-3