Compared with conventional minimization problems (e.g., empirical risk minimization), min-max optimization has aricher mathematical structure, thus being able tomodel more sophisticated learning problems thatemergefrom ever-emerging applications.

How does a human being distinguish the motions of a piece of paper and a piece of cloth? A high-school physics teacher might answer that they are both tangentially inextensible but cloth cannot resist any bending force from the normal direction.