Weak-subdifferentials for vector functions and applications to multiobjective semi-infinite optimization problems

ABSTRACT

A notion of generalized weak-subdifferentials for vector functions on a linear space is proposed. Properties of the weak-subdifferentials are investigated. A notion of weak-stability for a nonconvex optimization problems is introduced. Finally, relations between weak-stability and strong duality of the problem are established.

COMMUNICATED BY:

• Jen-Chih Yao

KEYWORDS:

• Weak-subgradient
• weak-subdifferential
• augmented Lagrangian vector function
• weak-stability
• strong duality

AMS SUBJECT CLASSIFICATIONS:

• 90C26
• 90C34
• 49N15
• 90C46

Acknowledgements

The authors would like to thank the anonymous referees for many valuable comments and suggestions to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was partially funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2017.08]. The second author was partially supported by the grant Ministry of Science and Technology, Taiwan (MOST) [106-2115-M-037- 001], and the grant from Research Center for Nonlinear Analysis and Optimization Kaohsiung Medical University, Taiwan [KMUOR106].