A discussion on the two kinds of definitions of linear bilevel programming solution

In order to well deal with a linear bilevel programming problem when the upper-level's constraint functions are of arbitrary linear form,Chenggen Shi gave a new definition of linear bilevel programming solution.This paper analyses the relationship between the new definition given by Chenggen Shi and the original definition of linear bilevel programming solution.A designed linear bilevel programming problem shows that under the two different definitions of linear bilevel programming solution,the same linear bilevel programming problem may have different optimal solutions.Then,this paper proposes the equivalent condition between the two kinds of definitions of linear bilevel programming solution.The example shows that the equivalent condition proposed above is correct.