Groupe d’études et de recherche en analyse des décisions

G-91-10

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 obtained. Reduction of more general global optimization problems than quadratic programs to bilinear programs is also briefly discussed.

, 29 pages

Ce cahier a été révisé en juin 1991