Titlebook: Bilevel Programming Problems; Theory, Algorithms a Stephan Dempe,Vyacheslav Kalashnikov,Nataliya Kala Book 2015 Springer-Verlag Berlin Heid

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978-3-662-51625-6Springer-Verlag Berlin Heidelberg 2015

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Introduction,istence of an optimal solution are formulated. Using a continuous knapsack problem with right-hand side perturbation in the lower level both formulations are illustrated. In the last part a number of applications of the problem are given.

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Reduction of Bilevel Programming to a Single Level Problem,evel 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 t

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Convex Bilevel Programs,eneral, a necessary optimality condition for a convex simple bilevel problem does not need to be sufficient. An adapted necessary and sufficient optimality condition is derived using tools from cone-convex optimization and a gradient type descent method is suggested which combines the use of a conve