Combining QCR and CHR for convex quadratic pure 0–1 programming problems with linear constraints

Aykut Ahlatçıoğlu (), Michael Bussieck (), Mustafa Esen (), Monique Guignard (), Jan-Hendrick Jagla () and Alexander Meeraus ()

Annals of Operations Research, 2012, vol. 199, issue 1, 33-49

Abstract: The convex hull relaxation (CHR) method (Albornoz in Doctoral Dissertation, 1998 , Ahlatçıoğlu in Summer paper, 2007 , Ahlatçıoğlu and Guignard in OPIM Dept. Report, 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 quadratic convex reformulation (QCR) method (2006), or one of its weaker predecessors designed for unconstrained problems, the eigenvalue method of Hammer and Rubin (RAIRO 3:67–79, 1970 ) or the method of Billionnet and Elloumi (Math. Program, Ser. A 109:55–68, 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. Copyright Springer Science+Business Media, LLC 2012

Keywords: Nonlinear integer programming; Bounds; Relaxation; Convex hull; CHR; QCR; SDP; GQAP (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10479-011-0969-1

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