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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\partial }_D\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>∂</mi> <mi>D</mi> </msub> </math></EquationSource> </InlineEquation>-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.</p>

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Optimality conditions and duality for multiobjective fractional bilevel optimization problems

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Felipe Lara,
  • Rishabh Pandey,
  • Vinay Singh

摘要

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 \({\partial }_D\) ∂ 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.