Proper efficiency in linear fractional vector optimization via Benson's characterization

Abstract

Linear fractional vector optimization problems are special non-convex vector optimization problems. They were introduced and first studied by E.U. Choo and D.R. Atkins in the period 1982–1984. This paper investigates the properness in the sense of Geoffrion of the efficient solutions of linear fractional vector optimization problems with unbounded constraint sets. Sufficient conditions for an efficient solution to be Geoffrion's properly efficient solution are obtained via Benson's characterization [An improved definition of proper efficiency for vector maximization with respect to cones. J Math Anal Appl. 1979;71:232–241] of Geoffrion's proper efficiency.

Keywords:

• Linear fractional vector optimization
• efficient solution
• Geoffrion's properly efficient solution
• Benson's characterization
• tangent cone

Acknowledgments

We are indebted to the two anonymous referees and the handling Associate Editor whose valuable suggestions have helped us to significantly improve the paper presentation. The first and the fourth authors would like to thank Vietnam Institute for Advanced Study in Mathematics (VIASM) for hospitality during their recent stay at the Institute.

Disclosure statement

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

Additional information

Funding

The authors were supported respectively by Le Quy Don Technical University (Vietnam), Kaohsiung Medical University (Taiwan), China Medical University (Taiwan), and the National Foundation for Science & Technology Development (Vietnam).