Fuzzy optimality conditions for fractional multi-objective problems

Abstract

In this article, we are concerned with fractional multi-objective optimization problems. Since those problems are in general nonconvex problems even if the problem data are convex, using techniques from variational analysis especially the approximate extremal principle [B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Series: Fundamental Principles of Mathematical Sciences, Vol. 330, Springer, Berlin, 2006; B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, II: Applications, Grundlehren Series: Fundamental Principles of Mathematical Sciences, Vol. 331, Springer, Berlin, 2006], we develop fuzzy optimality conditions.

Keywords:

• fractional optimization
• multi-objective optimization
• local weak efficient solution
• optimality conditions

AMS Subject Classifications::

• Primary 90C29
• Secondary 49K99

Acknowledgements

Our sincere thanks to the referees for their insightful remarks. This work has been supported by the Alexander-von Humboldt foundation.