On higher-order adjacent derivative of perturbation map in parametric vector optimization
Abstract This paper deals with higher-order sensitivity analysis in terms of the higher-order adjacent derivative for nonsmooth vector optimization. The relations between the higher-order adjacent derivative of the minima/the proper minima/the weak minima of a multifunction and its profile map are g...
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Online Access: | http://link.springer.com/article/10.1186/s13660-016-1059-3 |
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doaj-485ffac93ab54247b9845a6a86c6f8762020-11-24T21:17:59ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-04-012016111810.1186/s13660-016-1059-3On higher-order adjacent derivative of perturbation map in parametric vector optimizationLe Thanh Tung0Department of Mathematics, College of Natural Sciences, Can Tho UniversityAbstract This paper deals with higher-order sensitivity analysis in terms of the higher-order adjacent derivative for nonsmooth vector optimization. The relations between the higher-order adjacent derivative of the minima/the proper minima/the weak minima of a multifunction and its profile map are given. Then the relationships between the higher-order adjacent derivative of the perturbation map/the proper perturbation map/the weak perturbation map, and the higher-order adjacent derivative of a feasible map in objective space are considered. Finally, the formulas for estimating the higher-order adjacent derivative of the perturbation map, the proper perturbation map, the weak perturbation map via the adjacent derivative of the constraint map, and the higher-order Fréchet derivative of the objective map are also obtained.http://link.springer.com/article/10.1186/s13660-016-1059-3higher-order adjacent derivativeparameterized vector optimization problemperturbation mapproper perturbation mapweak perturbation maphigher-order sensitivity analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Le Thanh Tung |
spellingShingle |
Le Thanh Tung On higher-order adjacent derivative of perturbation map in parametric vector optimization Journal of Inequalities and Applications higher-order adjacent derivative parameterized vector optimization problem perturbation map proper perturbation map weak perturbation map higher-order sensitivity analysis |
author_facet |
Le Thanh Tung |
author_sort |
Le Thanh Tung |
title |
On higher-order adjacent derivative of perturbation map in parametric vector optimization |
title_short |
On higher-order adjacent derivative of perturbation map in parametric vector optimization |
title_full |
On higher-order adjacent derivative of perturbation map in parametric vector optimization |
title_fullStr |
On higher-order adjacent derivative of perturbation map in parametric vector optimization |
title_full_unstemmed |
On higher-order adjacent derivative of perturbation map in parametric vector optimization |
title_sort |
on higher-order adjacent derivative of perturbation map in parametric vector optimization |
publisher |
SpringerOpen |
series |
Journal of Inequalities and Applications |
issn |
1029-242X |
publishDate |
2016-04-01 |
description |
Abstract This paper deals with higher-order sensitivity analysis in terms of the higher-order adjacent derivative for nonsmooth vector optimization. The relations between the higher-order adjacent derivative of the minima/the proper minima/the weak minima of a multifunction and its profile map are given. Then the relationships between the higher-order adjacent derivative of the perturbation map/the proper perturbation map/the weak perturbation map, and the higher-order adjacent derivative of a feasible map in objective space are considered. Finally, the formulas for estimating the higher-order adjacent derivative of the perturbation map, the proper perturbation map, the weak perturbation map via the adjacent derivative of the constraint map, and the higher-order Fréchet derivative of the objective map are also obtained. |
topic |
higher-order adjacent derivative parameterized vector optimization problem perturbation map proper perturbation map weak perturbation map higher-order sensitivity analysis |
url |
http://link.springer.com/article/10.1186/s13660-016-1059-3 |
work_keys_str_mv |
AT lethanhtung onhigherorderadjacentderivativeofperturbationmapinparametricvectoroptimization |
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1726010968038703104 |