Article ID: | iaor20125549 |
Volume: | 199 |
Issue: | 1 |
Start Page Number: | 33 |
End Page Number: | 49 |
Publication Date: | Oct 2012 |
Journal: | Annals of Operations Research |
Authors: | Guignard Monique, Bussieck Michael, Meeraus Alexander, Ahlatiolu Aykut, Esen Mustafa, Jagla Jan-Hendrick |
Keywords: | programming: convex, programming: nonlinear |
The convex hull relaxation (CHR) method (Albornoz 2007; Ahlatçıoğlu and Guignard, 2010) provides lower bounds and feasible solutions on convex 0–1 nonlinear programming problems with linear constraints. In the quadratic case, these bounds may often be improved by a preprocessing step that adds to the quadratic objective function terms that are equal to 0 for all 0–1 feasible solutions yet increase its continuous minimum. Prior to computing CHR bounds, one may use Plateau’s (2006) quadratic convex reformulation (QCR) method , or one of its weaker predecessors designed for unconstrained problems, the eigenvalue method of Hammer and Rubin (1970) or the method of Billionnet and Elloumi (2007). In this paper, we first describe the CHR method, and then present the QCR reformulation methods. We present computational results for convex GQAP problems.