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DC programming techniques for solving a class of nonlinear bilevel programs

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Abstract

We propose a method for finding a global solution of a class of nonlinear bilevel programs, in which the objective function in the first level is a DC function, and the second level consists of finding a Karush-Kuhn-Tucker point of a quadratic programming problem. This method is a combination of the local algorithm DCA in DC programming with a branch and bound scheme well known in discrete and global optimization. Computational results on a class of quadratic bilevel programs are reported.

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Authors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, UFR MIM, Metz University, Ile du Saulcy, 57045, Metz, France

    Le Thi Hoai An

  2. Laboratory of Modelling, Optimization and Operations Research, LMI, National Institute for Applied Sciences - Rouen, BP 08, Place Emile Blondel F, 76131, Mont Saint Aignan Cedex, France

    Pham Dinh Tao & Nam Nguyen Canh

  3. Department of Mathematics, University of Trier, 54286, Trier, Germany

    Nguyen Van Thoai

Authors
  1. Le Thi Hoai An
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  2. Pham Dinh Tao
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  3. Nam Nguyen Canh
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  4. Nguyen Van Thoai
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Correspondence to Pham Dinh Tao.

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Hoai An, L.T., Tao, P.D., Nguyen Canh, N. et al. DC programming techniques for solving a class of nonlinear bilevel programs. J Glob Optim 44, 313–337 (2009). https://doi.org/10.1007/s10898-008-9325-7

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  • DOI: https://doi.org/10.1007/s10898-008-9325-7

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