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Discrete linear bilevel programming problem

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Abstract

In this paper, we analyze some properties of the discrete linear bilevel program for different discretizations of the set of variables. We study the geometry of the feasible set and discuss the existence of an optimal solution. We also establish equivalences between different classes of discrete linear bilevel programs and particular linear multilevel programming problems. These equivalences are based on concave penalty functions and can be used to design penalty function methods for the solution of discrete linear bilevel programs.

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Author notes

  1. L. Vicente (Lecturer)

    Present address: Department of Computational and Applied Mathematics, Rice University, Houston, Texas

Authors and Affiliations

  1. Departamento de Matemática, Universidade de Coimbra, Coimbra, Portugal

    L. Vicente (Lecturer) & J. Judice (Professor)

  2. Département de Mathématiques et Génie Industriel, Ecole Polytechnique de Montreal, Montreal, Quebec, Canada

    G. Savard (Professor)

Authors
  1. L. Vicente
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  2. G. Savard
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  3. J. Judice
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Additional information

Communicated by R. W. H. Sargent

Support of this work has been provided by the INIC (Portugal) under Contract 89/EXA/5, by INVOTAN, FLAD, and CCLA (Portugal), and by FCAR (Québec), NSERC, and DND-ARP (Canada).

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Vicente, L., Savard, G. & Judice, J. Discrete linear bilevel programming problem. J Optim Theory Appl 89, 597–614 (1996). https://doi.org/10.1007/BF02275351

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  • DOI: https://doi.org/10.1007/BF02275351

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