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This paper deals with a kind of nonconvex optimistic bilevel optimization programs. In some process of dealing this kind of bilevel programs, difficulties are essentially moved to estimating for coderivative of the solution map. To deal with these difficulties, we use value function of the lower level problem and its modifications as implicit functions to describe the solution map. By applying techniques in variational analysis, we give estimates for coderivative of the solution map. Then, we will show the applications in optimality conditions for these bilevel programs which we derived by using the extremal principle.

Estimates for coderivative of solution map in bilevel program