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Erschienen in:
2015 | OriginalPaper | Buchkapitel
5. Mixed-Integer Bilevel Programming Problems
verfasst von : Stephan Dempe, Vyacheslav Kalashnikov, Gerardo A. Pérez-Valdés, Nataliya Kalashnykova
Erschienen in: Bilevel Programming Problems
Verlag: Springer Berlin Heidelberg
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Abstract
Here we are faced with two more surprising facts: a global optimal solution of the linear relaxation of the mixed-discrete bilevel problem need not to be globally optimal even if it is feasible and an optimal solution of the optimistic linear bilevel problem does in general not exist. To circumvent the last difficulty, weak optimistic solutions are defined arising if the objective function is minimized over the closure of the feasible set. Optimality conditions can be defined using discontinuous, but piecewise continuously differentiable functions. In the last part, a solution algorithm is described using an outer approximation of the optimal value function of the lower level problem.