一类随机二层规划问题的近似求解方法收敛性分析

一类随机二层规划问题的近似求解方法收敛性分析 Convergence of Approximate Method for Solving Bilevel Stochastic Programming 王志强 WANG Zhi-qiang 1 2 first-author 万仲平 WAN Zhong-ping 1 2 池召艳 CHI Zhao-yan 1 2 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics, Wuhan University School of Mathematics and Statistics, Wuhan University 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 利用离散化的方法来处理连续型随机变量,将含有连续型随机变量的一类随机二层规划问题转化为一系列确定二层规划问题,证明了这种近似逼近问题的解上图收敛到原问题的解. This paper presents an approximate method for solving bilevel pro gramming.We transform original problem into a sequence of determinate problem by means of discretizing the continual random vector and a local decomposition method for solving the problem is proposed. Under some conditions, we have proved that the discretional solution epi-convergent to the solution of original problem. 随机二层规划 近似逼近 上图收敛 bilevel stochastic programming discretation epi-convergence O221.5 国家自然科学基金资助项目（70371032） 2005-01-01 2021-04-01 S2