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Global Search for Bilevel Optimization with Quadratic Data

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Bilevel Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 161))

Abstract

This chapter addresses a new methodology for finding optimistic solutions in bilevel optimization problems (BOPs). In Introduction, we present our view of the classification for corresponding numerical methods available in the literature. Then we focus on the quadratic case and describe the reduction of BOPs with quadratic objective functions to one-level nonconvex problems and develop methods of local and global searches for the reduced problems. These methods are based on the new mathematical tools of global search in nonconvex problems: the Global Search Theory (GST). A special attention is paid to a demonstration of the efficiency of the developed methodology for numerical solution of test BOPs.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics & Control Theory SB RAS, Irkutsk, Russia

    Alexander S. Strekalovsky & Andrei V. Orlov

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  1. Alexander S. Strekalovsky
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  2. Andrei V. Orlov
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Correspondence to Andrei V. Orlov .

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Editors and Affiliations

  1. Institute of Numerical Mathematics and Optimization, TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

  2. School of Mathematical Sciences, University of Southampton, Southampton, UK

    Alain Zemkoho

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Strekalovsky, A.S., Orlov, A.V. (2020). Global Search for Bilevel Optimization with Quadratic Data. In: Dempe, S., Zemkoho, A. (eds) Bilevel Optimization. Springer Optimization and Its Applications, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-030-52119-6_11

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