下层独立的一主多从双层随机线性规划问题研究

Stochastic Linear Bilevel Multi-Follower Programming with Independent Followers

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.

Herminia I. Calvete studied the linear bilevel multi-follower programming problem, and proved that this kind of problem can be converted into a linear bilevei 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 fol- lowers. 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 lhis type of problem in the practical application.