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- Publisher
- Springer Journals
- Copyright
- Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2022
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-022-1079-3
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential. We first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency, which used by the concepts of supremum and infimum of a set. We then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object map. Finally, we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization problem. In addition, we consider a generalized vector variational inequality as an application of abstract subdifferential.
Journal
"Acta Mathematicae Applicatae Sinica, English Series" – Springer Journals
Published: Apr 1, 2022
Keywords: Nonconvex set-valued vector optimization; abstract subdifferential; generalized augmented Lagrangian duality; exact penalization; sub-optimal path; 90C30; 90C46