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

Yihong Xu; Zhenhua Peng

doi:10.3934/jimo.2016019

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2017, Volume 13, Issue 1: 313-327. Doi: 10.3934/jimo.2016019

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

Yihong Xu^, and
Zhenhua Peng^,

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

Zhenhua Peng, E-mail: pzhjearya@gmail.com
Zhenhua Peng, E-mail: pzhjearya@gmail.com;
Zhenhua Peng, E-mail: pzhjearya@gmail.comYihong Xu, Professor, major field of interest is in the area of set-valued optimization. E-mail: xuyihong@ncu.edu.cn
Yihong Xu, Professor, major field of interest is in the area of set-valued optimization. E-mail: xuyihong@ncu.edu.cn

Received: March 31, 2015

Revised: November 30, 2015

Published: August 2017

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).

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Abstract

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.

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Mathematics Subject Classification: Primary: 49Q12, 46G05; Secondary: 90C31.

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References

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