Optimality Conditions and Duality for Multiobjective Fractional Bilevel Optimization Problems

TL;DR

This paper develops optimality conditions and duality theorems for multiobjective fractional bilevel optimization problems by reformulating them into single-level problems and applying nonsmooth analysis and generalized convexity concepts.

Contribution

It introduces refined optimality conditions and duality results for fractional bilevel problems using directional nonsmooth analysis and generalized convexity, advancing theoretical understanding.

Findings

Established necessary and sufficient optimality conditions.

Proved weak and strong duality theorems.

Illustrated advantages through examples.

Abstract

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 ${\partial}_D$-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.