Reduction of indefinite quadratic programs to bilinear programs
- Cite this article as:
- Hansen, P. & Jaumard, B. J Glob Optim (1992) 2: 41. doi:10.1007/BF00121301
- 154 Downloads
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.