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

Shan Cai; Shengxin Hua; Xiaoping Li; Shan Cai; Shengxin Hua; Xiaoping Li

doi:10.3934/math.2025813

AIMS Mathematics

2025, Volume 10, Issue 8: 18216-18231. doi: 10.3934/math.2025813

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

1.
College of Mathematics and Imformation Science, Xiangnan University, Chenzhou 423000, Hunan, China
2.
School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan 41105, Hunan, China

Received: 11 April 2025 Revised: 06 July 2025 Accepted: 24 July 2025 Published: 13 August 2025
MSC : 90C05, 90C30, 90C31

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.
- vector equilibrium,
- generalized convexity,
- optimality conditions,
- generating cones,
- scalarization theorems
Citation: Shan Cai, Shengxin Hua, Xiaoping Li. Optimality and scalarization for approximate Benson proper efficient solutions in vector equilibrium problems[J]. AIMS Mathematics, 2025, 10(8): 18216-18231. doi: 10.3934/math.2025813

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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.

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