On optimality conditions and duality for multiobjective fractional optimization problem with vanishing constraints

Haijun Wang; Gege Kang; Ruifang Zhang; Haijun Wang; Gege Kang; Ruifang Zhang

doi:10.3934/era.2024235

Electronic Research Archive

2024, Volume 32, Issue 8: 5109-5126. doi: 10.3934/era.2024235

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Research article

On optimality conditions and duality for multiobjective fractional optimization problem with vanishing constraints

School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, China

Received: 03 June 2024 Revised: 19 August 2024 Accepted: 22 August 2024 Published: 27 August 2024

The aim of this paper is to investigate the optimality conditions for a class of nonsmooth multiobjective fractional optimization problems subject to vanishing constraints. In particular, necessary and sufficient conditions for (weak) Pareto solution are presented in terms of the Clark subdifferential. Furthermore, we construct Wolfe and Mond–Weir-type dual models and derive some duality theorems by using generalized quasiconvexity assumptions. Some examples to show the validity of our conclusions are provided.
- multiobjective fractional optimization,
- vanishing constraint,
- locally Lipschitz function,
- duality theorems
Citation: Haijun Wang, Gege Kang, Ruifang Zhang. On optimality conditions and duality for multiobjective fractional optimization problem with vanishing constraints[J]. Electronic Research Archive, 2024, 32(8): 5109-5126. doi: 10.3934/era.2024235

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Abstract

The aim of this paper is to investigate the optimality conditions for a class of nonsmooth multiobjective fractional optimization problems subject to vanishing constraints. In particular, necessary and sufficient conditions for (weak) Pareto solution are presented in terms of the Clark subdifferential. Furthermore, we construct Wolfe and Mond–Weir-type dual models and derive some duality theorems by using generalized quasiconvexity assumptions. Some examples to show the validity of our conclusions are provided.

References

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