The Theory And Algorithm Of Bilevel Stochastic Multi-follower Programming

Bilevel programming is hierarchical optimization problem to study the two level decision making, widely appeared in the fields of economy, engineering and so on, research on this kind of problem has important theoretical and practical application value. In this paper, we consider the theory and algorithm of bilevei multi-follower programming problems, the specific work as follows:First, we summed up the research of theory and algorithm of deterministic bilevel multi-follower programming problems.Second, based on the result of Herminia and Garmen[1],we extended the determin-istic programming to stochastic programming, considered a special stochastic linear bileval programming problem with one leader and multiple followers. Under some special distribution cases of random variable, transformed the stochastic modle to de-terministic bilevel multi-follower programming problems, and turned it to a normal bilevel programming further, used the similar method of Herminia and Garmen[1], proofed the bilevel stochastic programming with independent multi-follower equivalent to the transformed normal bilevel programming. In the end, we studied algorithm of the transformed normal bilevel programming, used the KKT conditions turned the normal bilevel programming to nonlinear programming with one level, and proposed sequential quadratic programming algorithm to solve the final nolinear programming, then used numerical examples tested validity of algorithm.