Existence of Lagrange multipliers for set optimization with application to vector equilibrium problems

ABSTRACT

In this paper, we prove some results concerning the existence of the Lagrange multipliers for set optimization problems. Moreover, we indicate how these results may be applied to provide some optimality conditions for weak vector equilibrium problems.

Keywords:

• Set optimization
• oriented distance function
• Fritz John multipliers
• Karush–Kuhn–Tucker multipliers
• Vector equilibrium problems

2010 Mathematics Subject Classifications:

• 54C60
• 90C29
• 90C46
• 74G20

Acknowledgements

The authors are grateful to the Editor-in-chief, the Associate Editor as well as the two anonymous referees for their helpful suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.