Geoffrion proper efficiency in an infinite dimensional space

Abstract

We present a generalization of Geoffrions proper efficiency in the space

of continuous real-valued functions on a compact set T. As an important advantage, our definition keeps the componentwise structure used in the original definition. Further, we investigate the relations between our generalized Geoffrion proper efficiency and other types of proper efficiency such as those of Borwein and Benson or points received via linear scalarization.

Keywords:

• Vector-valued optimization
• Geoffrion proper efficiency
• Scalarization
• Infinite dimensional image space
• Mathematics Subject Classification 2000: 90C29
• 90C30

Acknowledgement

The author is grateful to an unknown referee for his comments and for indicating open questions which inspired further results.

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Kristin Winkler *

E-mail: [email protected]