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Bilevel Optimization: Reformulation and First Optimality Conditions

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Book cover Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

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Abstract

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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Authors and Affiliations

  1. TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

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  1. Stephan Dempe
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Correspondence to Stephan Dempe .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perpignan, Perpignan, France

    Didier Aussel

  2. Department of Mathematics, University of Delhi South Campus (UDSC), New Delhi, India

    C.S. Lalitha

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Dempe, S. (2017). Bilevel Optimization: Reformulation and First Optimality Conditions. In: Aussel, D., Lalitha, C. (eds) Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-4774-9_1

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