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

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.