Optimality and duality for a weakly efficient solution of bilevel multiobjective fractional programming problems with extremal-value function

Abstract

The purpose of this paper is to establish necessary and sufficient optimality conditions and some duality results for weakly efficient solutions of a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. Using parametric approach, the problem (P) is first equivalently transformed into a parametric problem (P µ) with µ ∈ Rp, for which we construct then a dual problem. This is achieved in terms of conjugate duality theory. Under appropriate assumptions, the weak and strong duality results for (Pµ) are presented. These results permit us to give dual characterizations for the weakly efficient solutions of the problem (P).

Keywords

• weakly efficient solution
• optimality conditions
• conjugate duality
• bilevel programming
• multiobjective fractional programming