  We propose a new method for solving the semidefinite (SD) relaxation of the
quadratic assignment problem (QAP), called Centering ADMM. Centering ADMM is an
alternating direction method of multipliers (ADMM) combining the centering
steps used in the interior-point method. The first stage of Centering ADMM
updates the iterate so that it approaches the central path by incorporating a
barrier function term into the objective function, as in the interior-point
method. If the current iterate is sufficiently close to the central path with a
sufficiently small value of the barrier parameter, the method switches to the
standard version of ADMM. We show that Centering ADMM (not employing a dynamic
update of the penalty parameter) has global convergence properties. To observe
the effect of the centering steps, we conducted numerical experiments with SD
relaxation problems of instances in QAPLIB. The results demonstrate that the
centering steps are quite efficient for some classes of instances.
