下层独立的一主多从双层随机线性规划问题研究

纪斌; 童小娇; 耿玉苹

下层独立的一主多从双层随机线性规划问题研究

引用本文：纪斌，童小娇，耿玉苹.下层独立的一主多从双层随机线性规划问题研究[J].经济数学,2016,(1):106-110

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作者	单位
纪斌，童小娇，耿玉苹	(1．湘潭大学数学与计算科学学院, 湖南湘潭411105； 2．湖南第一师范学院，湖南长沙410205； 3．湖南师范大学数学与计算机科学学院，湖南长沙410081）

中文摘要:Herminia I.Calvete等研究了一主多从双层确定性线性规划问题，证明了这类问题等价于一类常规的双层线性规划问题.本文在此基础上，推广确定型的问题到随机型优化情况，考虑了一类下层优化相互独立的一主多从双层随机优化问题(SLBMFP).在特定的随机变量分布条件下，理论上证明了该类问题可以转化为一主一从双层确定性优化问题.本文的研究对于求解一主多从双层随机优化模型，解决此类模型在实际应用中的问题具有一定的意义.

中文关键词:双层规划一主多从随机优化

Stochastic Linear Bilevel Multi-Follower Programming with Independent Followers

Abstract:Herminia I.Calvete studied the linear bilevel multi-follower programming problem, and proved that this kind of problem can be converted into a linear bilevel programming problem with one leader and one follower equivalently. And based on this result, this paper considered a special stochastic linear bileval programming problem with one leader and multiple followers. Under some special distribution cases of random variable, the addressed stochastic bilevel programming can be converted into a determinate bilevel programming problem with one leader and one follower. This paper is helpful in solving the bilevel multi-follower programming problem and this type of problem in the practical application.

keywords:bilevel programming multi-follower stochastic optimization

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