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Bilevel Linear Programming, Multiobjective Programming, and Monotonic Reverse Convex Programming

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Multilevel Optimization: Algorithms and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 20))

Abstract

The Bilevel Linear Programming problem and the problem of Linear Optimization over the Efficient Set are shown to be special forms of linear program with an additional reverse convex constraint having a monotonicity property. Exploiting this structure, one can convert the latter problem into a problem of much reduced dimension which can then be efficiently handled by d.c. programming decomposition methods.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, P.O Box 631, Bo Ho, Hanoi, Vietnam

    Hoang Thy

Authors
  1. Hoang Thy
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Editor information

Editors and Affiliations

  1. Division of Optimization, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden

    Athanasios Migdalas  & Peter Värbrand  & 

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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© 1998 Kluwer Academic Publishers

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Thy, H. (1998). Bilevel Linear Programming, Multiobjective Programming, and Monotonic Reverse Convex Programming. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) Multilevel Optimization: Algorithms and Applications. Nonconvex Optimization and Its Applications, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0307-7_13

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  • DOI: https://doi.org/10.1007/978-1-4613-0307-7_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7989-8

  • Online ISBN: 978-1-4613-0307-7

  • eBook Packages: Springer Book Archive

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