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Published in:
2015 | OriginalPaper | Chapter
3. Reduction of Bilevel Programming to a Single Level Problem
Authors : Stephan Dempe, Vyacheslav Kalashnikov, Gerardo A. Pérez-Valdés, Nataliya Kalashnykova
Published in: Bilevel Programming Problems
Publisher: Springer Berlin Heidelberg
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Abstract
Using the Karush-Kuhn-Tucker conditions, generalized equations describing necessary optimality conditions or the optimal value function of the lower level problem, the bilevel optimization problem can be transformed into a single-level optimization problem. Two of these transformations are fully equivalent to the bilevel problem, the MPEC is not. Using these transformations, necessary conditions for local optimal solutions can be formulated: In the case of a strongly stable lower level optimal solution using its directional derivative, using partial calmness in the optimal value function transformation, and applying variational analysis for KKT transformations explicitly using Lagrange multipliers or not. Solution algorithms are formulated and investigated for all reductions.