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The Local and Global Searches in Bilevel Problems with a Matrix Game at the Lower Level

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

This work addresses the simplest class of the bilevel optimization problems (BOPs) with equilibrium at the lower level. We study linear BOPs with a matrix game at the lower level in their optimistic statement. First, we transform this problem to a single-level nonconvex optimization problem with the help of the optimality conditions for the lower level problem. Then we apply the special Global Search Theory (GST) for general d.c. optimization problems to the reduced problem. Following this theory, the methods of local and global searches in this problem are constructed. These methods take into account the structure of the problem in question.

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Authors and Affiliations

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

    Andrei V. Orlov & Tatiana V. Gruzdeva

Authors
  1. Andrei V. Orlov
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  2. Tatiana V. Gruzdeva
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Correspondence to Andrei V. Orlov .

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Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Orlov, A.V., Gruzdeva, T.V. (2019). The Local and Global Searches in Bilevel Problems with a Matrix Game at the Lower Level. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_13

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

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