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

  • Andrei V. OrlovEmail author
  • Tatiana V. Gruzdeva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Bilevel optimization Bilevel problems with equilibrium at the lower level Matrix game Optimistic solution Reduction theorem D.C. constraint problem Global Search Theory Local search Global search 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control Theory of SB of RASIrkutskRussia

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