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Global Search for Bilevel Optimization with Quadratic Data

In: Bilevel Optimization

Author

Listed:
  • Alexander S. Strekalovsky

    (Matrosov Institute for System Dynamics & Control Theory SB RAS)

  • Andrei V. Orlov

    (Matrosov Institute for System Dynamics & Control Theory SB RAS)

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.

Suggested Citation

  • Alexander S. Strekalovsky & Andrei V. Orlov, 2020. "Global Search for Bilevel Optimization with Quadratic Data," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 313-334, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-52119-6_11
    DOI: 10.1007/978-3-030-52119-6_11
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