NDLI: Eigenvalue Bounds Versus Semidefinite Relaxations for the Quadratic Assignment Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Anstreicher, K. M.
Copyright Year	2000
Abstract	It was recently demonstrated that a well-known eigenvalue bound for the quadratic assignment problem (QAP) actually corresponds to a semidefinite programming (SDP) relaxation. However, for this bound to be computationally useful, the assignment constraints of the QAP must first be eliminated and the bound then applied to a lower-dimensional problem. The resulting "projected eigenvalue bound" is one of the best available bounds for the QAP, especially when considering the quality of bounds relative to the complexity of obtaining them. In this paper we show that the projected eigenvalue bound is also related to an SDP relaxation of the original QAP. This "implicit" SDP relaxation is similar to SDP relaxations of the QAP proposed by Lin and Saigal [On Solving Large-scale Semidefinite Programming Problems---A Case Study of Quadratic Assignment Problem, Department of Industrial Engineering and Operations Research, University of Michigan, 1997] and Zhao et al. [J. Combin. Optim., 2 (1998), pp. 71-109].
Starting Page	254
Ending Page	265
Page Count	12
File Format	PDF
ISSN	10526234
DOI	10.1137/S1052623499354904
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	1
Volume Number	11
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	semidefinite programming Boolean programming quadratic assignment problem eigenvalue bounds Quadratic programming
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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