This paper focuses on the problem of hyper-graph matching, by accounting for both unary and higher-order affinity terms. Our method is in line with the linear approximate framework while the problem is iteratively solved in discrete space. It is empirically found more efficient than many extant continuous methods. Moreover, it avoids unknown accuracy loss by heuristic rounding step from the continuous approaches. Under weak assumptions, we prove the iterative discrete gradient assignment in general will trap into a degenerating case - an m-circle solution path where m is the order of the problem. A tailored adaptive relaxation mechanism is devised to detect the degenerating case and makes the algorithm converge to a fixed point in discrete space. Evaluations on both synthetic and real-world data corroborate the efficiency of our method.