Image regularity conditions for nonconvex multiobjective optimization problems with applications

Abstract

The main purpose of this paper is to investigate Lagrange saddle points and calmness properties for a nonconvex multiobjective optimization problem by virtue of image regularity conditions. Following along with the image space analysis, the quasi-interior, quasi-relative interior and linear image regularity conditions are presented. Simultaneously, some equivalent characterizations to Fritz John and Karush/Kuhn-Tucker saddle points are established respectively by virtue of the proposed image regularity conditions. Moreover, some calmness properties are also obtained by means of local conic image regularity conditions in the image space of the multiobjective optimization problem.

Keywords:

• Multiobjective optimization
• image space analysis
• image regularity condition
• Lagrange saddle point
• calmness

Mathematics Subject Classifications (2020):

• 90C26
• 90C29
• 49N15

Acknowledgments

The authors are grateful to the anonymous Associate Editor and the three Reviewers for their valuable comments and suggestions, which help to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 11601437], the Scientific Research Fund of Sichuan Provincial Science and Technology Department [grant number 2021YJ0524] and the Fundamental Research Funds for the Central Universities [grant number JBK2202043].