Optimality conditions and duality for multiobjective fractional bilevel optimization problems

This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These results are derived using ∂D-nonsmooth Abadie-type constraint qualifications and generalized convexity concepts (quasiconvexity and pseudoconvexity) based on directional convexificators. We also prove weak and strong duality theorems for a Mond–Weir dual problem formulated with directional convexificators. Finally, several examples are provided to illustrate the advantages of our approach.