Infinite-dimensional vector optimization and a separation theorem

ABSTRACT

Using relative minimality solutions for vector optimization problems, we establish optimality conditions in terms of Karush–Kuhn–Tucker multipliers as well as Fritz-John multipliers. Moreover, we give a general separation theorem including both finite and infinite classical separation theorem.

Keywords:

• Compactly epi-Lipschitzian set
• vector optimization
• separation theorem
• quasi-relative solution
• Karush–Kuhn–Tucker multipliers

2010 Mathematics Subject Classifications:

• 90C25
• 46A20

View correction statement:

Corrigendum to ‘Infinite-dimensional vector optimization and a separation theorem’

Acknowledgments

The authors would like to thank 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 author(s).