  We study the quadratic assignment problem, in computer vision also known as
graph matching. Two leading solvers for this problem optimize the Lagrange
decomposition duals with sub-gradient and dual ascent (also known as message
passing) updates. We explore s direction further and propose several additional
Lagrangean relaxations of the graph matching problem along with corresponding
algorithms, which are all based on a common dual ascent framework. Our
extensive empirical evaluation gives several theoretical insights and suggests
a new state-of-the-art any-time solver for the considered problem. Our
improvement over state-of-the-art is particularly visible on a new dataset with
large-scale sparse problem instances containing more than 500 graph nodes each.
