集值均衡问题的$E_{\infty }$-Benson真有效解的非线性标量化

Nonlinear Scalarization of the Properly Effective $E_{\infty }$-Benson Solution for the Equilibrium Problem with Set-Valued Maps

摘要: 众所周知，在最优化理论中，集值均衡问题是一个关键组成部分，它在数理经济和交通系统等实际应用中具有重要的研究意义和理论价值。许多学者从不同的角度提出了集值均衡问题不同类型的解。然而，如何推广和改进集值均衡问题的解是有意义的。本文，我们利用改进集和回收锥这两种研究最优化理论的重要工具，研究了带约束集值均衡问题的E∞-Benson真有效解，建立了集值均衡问题的非线性标量化定理。

Abstract: As is well-known in optimization theory, the problem of set-valued equilibrium is a key component. It holds significant research significance and theoretical value in practical applications such as mathematical economics and transportation systems. Many scholars have proposed various types of solutions to the set-valued equilibrium problem from different perspectives. However, the meaningful task lies in generalizing and improving the solutions to the set-valued equilibrium problem. In this paper, utilizing the improvement set and the recession cone which are two important tools to study optimization theory, we investigateE∞-Benson properly efficient solution of the set-valued equilibrium problem. Furthermore, we establish the nonlinear scalarization theorems of the set-valued equilibrium problem.