Journal of Global Optimization

, Volume 2, Issue 1, pp 41–60

Reduction of indefinite quadratic programs to bilinear programs

  • Pierre Hansen
  • Brigitte Jaumard
Article

DOI: 10.1007/BF00121301

Cite this article as:
Hansen, P. & Jaumard, B. J Glob Optim (1992) 2: 41. doi:10.1007/BF00121301

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.

Key words

Quadratic program bilinear program global optimization reduction 

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Pierre Hansen
    • 1
    • 2
  • Brigitte Jaumard
    • 3
    • 4
  1. 1.Ecole des Hautes Études Commerciales, Département des Méthodes Quantitatives et Systèmes d'InformationGERADMontréalCanada
  2. 2.RUTCORRutgers UniversityU.S.A.
  3. 3.Department of Civil Engineering and Operations ResearchPrinceton UniversityU.S.A.
  4. 4.Ecole Polytechnique de Montréal, Département de Mathématiques AppliquéesGERADMontréalCanada