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Research Article | Open Access

Optimality and scalarization for approximate Benson proper efficient solutions in vector equilibrium problems

Shan Cai1, Shengxin Hua2( ), Xiaoping Li1
College of Mathematics and Imformation Science, Xiangnan University, Chenzhou 423000, Hunan, China
School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan 41105, Hunan, China
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Abstract

This paper examines the optimality and scalarization theorems for approximate quasi-Benson proper efficient solutions in constrained vector equilibrium problems. The optimality conditions are established based on the generalized convexity and convex separation theorems. Additionally, two scalarization theorems are developed by combining the cone scalarization function with the properties of generating cones. The proposed definitions and conclusions are supported by specific numerical examples.

Keywords

vector equilibriumgeneralized convexityoptimality conditionsgenerating conesscalarization theorems
CLC number: 90C05, 90C30, 90C31

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AIMS Mathematics
Volume 10 Issue 8,
August 2025
Pages 18216-18231
DOI: 10.3934/math.2025813

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Cite this article:
Cai S, Hua S, Li X. Optimality and scalarization for approximate Benson proper efficient solutions in vector equilibrium problems. AIMS Mathematics, 2025, 10(8): 18216-18231. https://doi.org/10.3934/math.2025813

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Received: 11 April 2025
Revised: 06 July 2025
Accepted: 24 July 2025
Published: 15 August 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)