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doi: 10.3934/jimo.2020176

## Perturbation of Image and conjugate duality for vector optimization

 1 College of Mathematics and Information, China West Normal University, Nanchong 637009, Sichuan, China 2 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

* Corresponding author: Manxue You

Received  January 2019 Revised  October 2019 Published  December 2020

Fund Project: This research was supported by the National Natural Science Foundation of China (Grant numbers: 12001438, 11971078, 11871059) and the Fund of China West Normal University (NO. 18Q059, 19B043)

This paper aims at employing the image space approach to investigate the conjugate duality theory for general constrained vector optimization problems. We introduce the concepts of conjugate map and subdifferential by using two types of maximums. We also construct the conjugate duality problems via a perturbation method. Moreover, the separation condition is proposed by means of vector weak separation functions. Then, it is proved to be a new sufficient condition, which ensures the strong duality theorem. This separation condition is different from the classical regular conditions in the literature. Simultaneously, the application to a nonconvex multi-objective optimization problem is shown to verify our main results.

Citation: Manxue You, Shengjie Li. Perturbation of Image and conjugate duality for vector optimization. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020176
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The red curve shows the set of objective function values
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