On higher-order adjacent derivative of perturbation map in parametric vector optimization

• Main Author: Le Thanh Tung
• Format: Article
• Language: English
• Published: SpringerOpen 2016-04-01
• Series: Journal of Inequalities and Applications
• Subjects: higher-order adjacent derivative; parameterized vector optimization problem; perturbation map; proper perturbation map; weak perturbation map; higher-order sensitivity analysis
• Online Access: http://link.springer.com/article/10.1186/s13660-016-1059-3

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.