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

为研究二层多目标随机规划逼近问题的弱有效解与精确的弱有效解之间的逼近收敛性,针对上、下层都带有约束条件的一类多目标二层随机规划的逼近问题,构建了二层多目标随机规划逼近问题的弱有效解集的上半收敛性理论框架。即在假设下层反馈到上层的最优解集函数为凸函数的前提下,借助严格凸函数的性质,利用多目标随机规划的弱有效解可以表示成相应的单目标随机规划最优解集交集的结构特征,建立了二层多目标随机规划逼近弱有效解集的上半收敛性,提供了逼近方法求解二层多目标随机规划弱有效解集可以近似替代精确的弱有效解集的理论依据。

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 optimal 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-objective 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.