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February  2017, 13(1): 313-327. doi: 10.3934/jimo.2016019

## Higher-order sensitivity analysis in set-valued optimization under Henig efficiency

 Department of Mathematics, Nanchang University, Nanchang, 330031, China

Yihong Xu, Professor, major field of interest is in the area of set-valued optimization. E-mail: xuyihong@ncu.edu.cn

Zhenhua Peng, E-mail: pzhjearya@gmail.com

Received  April 2015 Revised  December 2015 Published  March 2016

Fund Project: the National Natural Science Foundation of China Grant 11461044, the Natural Science Foundation of Jiangxi Province (20151BAB201027) and the Science and Technology Foundation of the Education Department of Jiangxi Province(GJJ12010).

The behavior of the perturbation map is analyzed quantitatively by using the concept of higher-order contingent derivative for the set-valued maps under Henig efficiency. By using the higher-order contingent derivatives and applying a separation theorem for convex sets, some results concerning higher-order sensitivity analysis are established.

Citation: Yihong Xu, Zhenhua Peng. Higher-order sensitivity analysis in set-valued optimization under Henig efficiency. Journal of Industrial & Management Optimization, 2017, 13 (1) : 313-327. doi: 10.3934/jimo.2016019
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