Open AccessPerturbation of Image and conjugate duality for vector optimization
Author(s) -
Manxue You,
Shengjie Li
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2020176
Subject(s) - duality (order theory) , perturbation function , vector optimization , mathematics , conjugate , subderivative , conjugate gradient method , perturbation (astronomy) , vector space , optimization problem , strong duality , duality gap , mathematical optimization , pure mathematics , mathematical analysis , convex analysis , convex optimization , geometry , regular polygon , physics , multi swarm optimization , quantum mechanics
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.