Bilevel programming with discrete lower level problems

In this article, we investigate bilevel programming problems with discrete lower level and continuous upper level problems. We will analyse the structure of these problems and discuss both the optimistic and the pessimistic solution approach. Since neither the optimistic nor the pessimistic solution functions are in general lower semicontinuous, we introduce weak solution function. By using these functions we are able to discuss optimality conditions for local and global optimality.

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