纺织高校基础科学学报2024，Vol.37Issue(3)：118-124,7.DOI:10.13338/j.issn.1006-8341.2024.03.014
二层多目标随机规划逼近弱有效解集的上半收敛性
The upper semi-convergence of the set of approximation weakly efficient solutions for bi-level multi-objective stochastic programming
摘要
Abstract
In order to study the convergence of approximation between the exact weakly efficient solution and the weakly efficient solution of the approximation problem of bi-level multi-objective stochastic programming,we construct an upper semi-convergence theoretical framework of weakly efficient solution sets for a class of approximation problems of multi-objective bi-level stochastic programming with both upper and lower constraints.In other words,on the premise of assuming that the optimal solution set function fed back from the lower layer to the upper layer is convex function,using the property of strict convex function,the weakly efficient solution of multi-objective stochastic programming can be expressed as the structural feature of the intersection of the opti-mal solution set of the corresponding single objective stochastic programming,and the upper semi-convergence of the approximation of the weakly efficient solution set by the bi-level multi-objec-tive stochastic programming is established.This conclusion provides the theorectical basis that approximation weakly effective solution sets can approximately replace the exact weakly effective solution sets in bi-level multi-objective stochastic programming.关键词
单目标随机规划/多目标随机规划/弱有效解集/严格凸函数Key words
single objective stochastic programming/multi-objective stochastic programming/weakly efficient solution sets/strictly convex function分类
数理科学引用本文复制引用
周婉娜,霍永亮..二层多目标随机规划逼近弱有效解集的上半收敛性[J].纺织高校基础科学学报,2024,37(3):118-124,7.基金项目
陕西省科技厅自然科学基础研究项目(2022JQ-712) （2022JQ-712）
西安翻译学院科研项目(23B21) （23B21）
