Perturbation of Image and conjugate duality for vector optimization

Manxue You; Shengjie Li

doi:10.3934/jimo.2020176

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2022, Volume 18, Issue 2: 731-745. Doi: 10.3934/jimo.2020176

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Perturbation of Image and conjugate duality for vector optimization

Manxue You^1, , and
Shengjie Li^2,

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
^* Corresponding author: Manxue You

Received: January 2019

Revised: October 2019

Early access: December 2020

Published: March 2022

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).

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Abstract

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.

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Mathematics Subject Classification: 90C26;90C29;90C46.

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