集值优化问题弱极小解的逼近定理
Approximation Theorem for Weak Minimal Solutions of Set-Valued Optimization Problems
DOI: 10.12677/PM.2024.142065, PDF,   
作者: 伍玉涛：贵州大学数学与统计学院，贵州 贵阳
关键词: 集值优化问题；有限理性；逼近定理；Set-Valued Optimization Problems； Bounded Rationality； Approximation Theorem
摘要: 目的：针对集值优化问题，考虑该问题的近似弱极小解序列的收敛性。方法：通过定义集值优化问题的ε-近似弱极小解的概念，在有限理性的框架下寻求一个集值优化问题的近似弱极小解序列来逼近其精确解。结果：给出了集值优化问题弱极小解的一个逼近定理以及两个重要推论。结论：证明了在一定条件下对于集值优化问题可以用在有限理性下的近似解来逼近在完全理性下的精确解，这一结果为该问题的计算提供了一种理论支持。
Abstract: Objective: For set-valued optimization problem, we consider the convergence of the approximate weak minimal solution sequence. Method: By defining the concept of ε-approximate weak minimal solution for set-valued optimization problems, we aim to seek a sequence of approximate weak minimal solutions for the problem to approximate their exact solutions. Results: An approximation theorem and two corollaries for set-valued optimization problems are presented. Conclusion: It is proved that under certain conditions, the approximate solution under bounded rationality can be approached by the exact solution under full rationality for set-valued optimization problems. This result provides a theoretical support for the calculation of the problem.
文章引用：伍玉涛. 集值优化问题弱极小解的逼近定理[J]. 理论数学, 2024, 14(2): 655-660. https://doi.org/10.12677/PM.2024.142065

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