Journal of Global Optimization

, Volume 43, Issue 2, pp 471-484

First online:

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

  • Kurt M. AnstreicherAffiliated withDepartment of Management Sciences, Tippie College of Business, University of Iowa Email author 

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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.


Semidefinite programming Reformulation-linearization technique Quadratically constrained quadratic programming

AMS Subject Classifications

90C26 90C22