Sensitivity analysis in set-valued optimization under strictly minimal efficiency

Zhenhua Peng; Zhongping Wan; Weizhi Xiong

doi:10.3934/eect.2017022

Article Contents

2017, Volume 6, Issue 3: 427-436. Doi: 10.3934/eect.2017022

This issue Previous Article $\mathbb{L}^p-$solutions of the stochastic Navier-Stokes equations subject to Lévy noise with $\mathbb{L}^m(\mathbb{R}^m)$ initial data Next Article Long-time dynamics for a class of extensible beams with nonlocal nonlinear damping^*

Sensitivity analysis in set-valued optimization under strictly minimal efficiency

1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
2.
College of Mathematics and Science, Tongren University, Tongren 554300, China

* Corresponding author: pzhjearya@gmail.com
* Corresponding author: pzhjearya@gmail.com

Received: November 30, 2015

Revised: April 30, 2017

Published: October 2017

The authors are supported by the Natural Science Foundation of China No. 71471140, Natural science program of Guizhou Provincial Department of Education[2015]456 and Collaborative Fund of the Science and Teachnology Department of Guizhou Province[2014]7490.

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Abstract

In this paper, the behavior of the perturbation map is analyzed quantitatively by virtue of contingent derivatives and generalized contingent epiderivatives for the set-valued maps under strictly minimal efficiency. The purpose of this paper is to provide some well-known results concerning sensitivity analysis by applying a separation theorem for convex sets. When the results regress to multiobjective optimization, some related conclusions are obtained in a multiobjective programming problem.

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Mathematics Subject Classification: Primary: 90C29, 46G05; Secondary: 49Q12.

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References

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