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Perturbation of Image and conjugate duality for vector optimization

  • * Corresponding author: Manxue You

    * Corresponding author: Manxue You 

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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  • 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.

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


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  • Figure 1.  The red curve shows the set of objective function values

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