Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming

We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulation-linearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial port...

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Bibliographic Details
Published in:Journal of global optimization Vol. 43; no. 2-3; pp. 471 - 484
Main Author: Anstreicher, Kurt M.
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2009
Springer Nature B.V
Subjects:
Computer Science
Inequality
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Symmetry
Variables
Semidefinite programming
90C26
Quadratically constrained quadratic programming
Reformulation-linearization technique
90C22
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulation-linearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial portion of the feasible region corresponding to product terms in the RLT relaxation. On test problems we show that the use of SDP and RLT constraints together can produce bounds that are substantially better than either technique used alone. For highly symmetric problems we also consider the effect of symmetry-breaking based on tightened bounds on variables and/or order constraints.
Bibliography:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-008-9372-0