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A Study of Local Solutions in Linear Bilevel Programming

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Abstract

In this paper, a linear bilevel programming problem (LBP) is considered. Local optimality in LBP is studied via two related problems (P) and P(M). Problem (P) is a one-level model obtained by replacing the innermost problem of LBP by its KKT conditions. Problem P(M) is a penalization of the complementarity constraints of (P) with a penalty parameter M. Characterizations of a (strict) local solution of LBP are derived. In particular, the concept of equilibrium point of P(M) is used to characterize the local optima of (P) and LBP.

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Authors and Affiliations

  1. Professor, Departamento de Estatística e Matemática Aplicada, Universidade Federal do Ceará, Fortaleza, Ceará, Brazil

    M. Campêlo

  2. Professor, DCC/IM, COPPE/Sistemas, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    S. Scheimberg

Authors
  1. M. Campêlo
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  2. S. Scheimberg
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Additional information

Research partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. The authors thank theanonymous referees for careful reading and useful suggestions.

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Campêlo, M., Scheimberg, S. A Study of Local Solutions in Linear Bilevel Programming. J Optim Theory Appl 125, 63–84 (2005). https://doi.org/10.1007/s10957-004-1711-9

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  • DOI: https://doi.org/10.1007/s10957-004-1711-9

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