Bilevel Optimization: Reformulation and First Optimality Conditions

  • Stephan Dempe
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)


Bilevel optimization problems are nonsmooth, nonconvex optimization problems the feasible set of which is (in part) described using the graph of the solution set mapping of a second parametric optimization problem. To investigate them, their transformation into a one-level optimization problem is necessary. For that, different approaches can be used. Two of them are considered in this article: the transformation using the Karush–Kuhn–Tucker conditions of the (convex) lower level problem resulting in a mathematical program with equilibrium constraint (MPEC) and the use of the optimal value function of this problem which leads to a nonsmooth optimization problem. Besides the resulting necessary optimality conditions, first solution algorithms for the bilevel problem using these transformations are presented.


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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.TU Bergakademie FreibergFreibergGermany

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