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Reduction of indefinite quadratic programs to bilinear programs

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Abstract

Indefinite quadratic programs with quadratic constraints can be reduced to bilinear programs with bilinear constraints by duplication of variables. Such reductions are studied in which: (i) the number of additional variables is minimum or (ii) the number of complicating variables, i.e., variables to be fixed in order to obtain a linear program, in the resulting bilinear program is minimum. These two problems are shown to be equivalent to a maximum bipartite subgraph and a maximum stable set problem respectively in a graph associated with the quadratic program. Non-polynomial but practically efficient algorithms for both reductions are thus obtaine.d Reduction of more general global optimization problems than quadratic programs to bilinear programs is also briefly discussed.

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Authors and Affiliations

  1. Ecole des Hautes Études Commerciales, Département des Méthodes Quantitatives et Systèmes d'Information, GERAD, 5255 avenue Decelles, H3T1V6, Montréal, Canada

    Pierre Hansen

  2. RUTCOR, Rutgers University, 08904, New Jersey, U.S.A.

    Pierre Hansen

  3. Department of Civil Engineering and Operations Research, Princeton University, 08544-5263, New Jersey, U.S.A.

    Brigitte Jaumard

  4. Ecole Polytechnique de Montréal, Département de Mathématiques Appliquées, GERAD, Succursale A, Case Postale 6079, H3C 3A7, Montréal, Québec, Canada

    Brigitte Jaumard

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Hansen, P., Jaumard, B. Reduction of indefinite quadratic programs to bilinear programs. J Glob Optim 2, 41–60 (1992). https://doi.org/10.1007/BF00121301

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  • DOI: https://doi.org/10.1007/BF00121301

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