Copositive and semidefinite relaxations of the quadratic assignment problem

Janez Povh (Author), Franz Rendl (Author)

Abstract

Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look at tractable approximations and compare with several relaxations from the literature. We show that several of the well-studied models are in fact equivalent. It is still a challenging task to solve the strongest of these models to reasonable accuracy on instances of moderate size.

Keywords

matematično programiranje;problem kvadratičnega prirejanja;kopozitivno programiranje;semidefinitna poenostavitev;quadratic assignment problem;copositive programming;semidefinite relaxations;lift-and-project relaxations;

Data

Language:	English
Year of publishing:	2009
Typology:	1.01 - Original Scientific Article
Organization:	UM FL - Faculty of Logistics
UDC:	519.85
COBISS:	15143001
ISSN:	1572-5286
Views:	28
Downloads:	21
Average score:	0 (0 votes)
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