A note on reduction of quadratic and bilinear programs with equality constraints

Authors:
Jack Brimberg;Pierre Hansen;Nenad Mladenović/
Affiliations:
School of Business Administration, University of Prince Edward Island, Charlottetown (PEI), Canada and GERAD/;GERAD, É/cole des Hautes É/tudes Commerciales, Montré/al, Canada and Hong Kong Polytechnic (E-mail: pierreh@crt.umontreal.ca)/Corresponding author;Mathematical Institute, Serbian Academy of Science, Belgrade, Yugoslavia and GERAD
Venue:
Journal of Global Optimization
Year:
2002

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Abstract

Reduction of some classes of global optimization programs to bilinear programs may be done in various ways, and the choice of method clearly influences the ease of solution of the resulting problem. In this note we show how linear equality constraints may be used together with graph theoretic tools to reduce a bilinear program, i.e., eliminate variables from quadratic terms to minimize the number of complicating variables. The method is illustrated on an example. Computer results are reported on known test problems.