Iceberg-cube mining is to compute the GROUP BY partitions, for all GROUP BY dimension lists, that satisfy a given aggregate constraint. Previous works have pushed anti-monotone constraints into iceberg-cube mining. However, many useful constraints are not anti-monotone. In this paper, we propose a novel strategy for pushing general aggregate constraints, called Divide-and-Approximate. This strategy divides the search space and approximates the constraint in subspaces by a pushable constraint. As the strategy is recursively applied, the approximation approaches the given constraint and the pruning tights up. We show that all constraints defined by SQL aggregates, arithmetic operators and comparison operators can be pushed by Divide-and-Approximate. We present an efficient implementation for an important subclass and evaluate it on both synthetic and real life databases.