Reduction of indefinite quadratic programs to bilinear programs
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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.
- Reduction of indefinite quadratic programs to bilinear programs
Journal of Global Optimization
Volume 2, Issue 1 , pp 41-60
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- Kluwer Academic Publishers
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- Quadratic program
- bilinear program
- global optimization
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- Author Affiliations
- 1. Ecole des Hautes Études Commerciales, Département des Méthodes Quantitatives et Systèmes d'Information, GERAD, 5255 avenue Decelles, H3T1V6, Montréal, Canada
- 2. RUTCOR, Rutgers University, 08904, New Jersey, U.S.A.
- 3. Department of Civil Engineering and Operations Research, Princeton University, 08544-5263, New Jersey, U.S.A.
- 4. Ecole Polytechnique de Montréal, Département de Mathématiques Appliquées, GERAD, Succursale A, Case Postale 6079, H3C 3A7, Montréal, Québec, Canada