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A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points

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Abstract

In this paper, a linear bilevel programming problem (LBP) is considered. Local optimality conditions are derived. They are based on the notion of equilibrium point of an exact penalization for LBP. It is described how an equilibrium point can be obtained with the simplex method. It is shown that the information in the simplex tableaux can be used to get necessary and sufficient local optimality conditions for LBP. Based on these conditions, a simplex type algorithm is proposed, which attains a local solution of LBP by moving in equilibrium points. A numerical example illustrates how the algorithm works. Some computational results are reported.

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Authors and Affiliations

  1. Dep. de Estatística e Mat. Aplicada, Universidade Federal do Ceará—UFC, CEP 60455-760, Fortaleza-CE, Brazil

    Manoel Campêlo

  2. DCC/IM, COPPE/Sistemas, Universidade Federal do Rio de Janeiro—UFRJ, Brazil

    Susana Scheimberg

Authors
  1. Manoel Campêlo
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  2. Susana Scheimberg
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Correspondence to Manoel Campêlo.

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Campêlo, M., Scheimberg, S. A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points. Ann Oper Res 138, 143–157 (2005). https://doi.org/10.1007/s10479-005-2450-5

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  • DOI: https://doi.org/10.1007/s10479-005-2450-5

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