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Abstract

In the paper, we study the generalized differentiability in set-valued optimization, namely stydying the second-order composed radial derivative of a given set-valued mapping. Inspired by the adjacent cone and the higher-order radial con in Anh NLH et al. (2011), we introduce the second-order composed radial derivative.  Then, its basic properties are investigated and relationships between the second-order compsoed radial derivative of a given set-valued mapping and that of its profile are obtained. Finally, applications of this derivative to sensitivity analysis are studied. In detail, we work on a parametrized set-valued optimization problem concerning Pareto solutions.  Based on the above-mentioned results, we find out sensitivity analysis for Pareto solution mapping of the problem. More precisely, we establish the second-order composed radial derivative for the perturbation mapping (here, the perturbation means the Pareto solution mapping concerning some parameter). Some examples are given to illustrate our results. The obtained results are new and improve the existing ones in the literature.



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Article Details

Issue: Vol 4 No 3 (2020): Under Publishing
Page No.: 567-572
Published: Jul 1, 2020
Section: Original Research
DOI: https://doi.org/10.32508/stdjns.v4i3.838

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Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Ngọc, P. L., Tung, N., & Nghia, N. (2020). The second-order composed radial derivatives of perturbation mappings of parametric set-valued optimization problems. Science and Technology Development Journal - Natural Sciences, 4(3), 567-572. https://doi.org/https://doi.org/10.32508/stdjns.v4i3.838

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