We present a convex relaxation for the multi-graph matching problem. Our formulation allows for partial pairwise matchings, guarantees cycle consistency, and our objective incorporates both linear and quadratic costs. Moreover, we also present an extension to higher-order costs. In order to solve the convex relaxation we employ a message passing algorithm that optimizes the dual problem. We experimentally compare our algorithm on established benchmark problems from computer vision, as well as on large problems from biological image analysis, the size of which exceed previously investigated multi-graph matching instances.