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Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify and deal with the fundamental difficulties this poses. In this paper, we study the classic proximal point method (PPM) applied to nonconvex-nonconcave minimax problems. We find that a classic generalization of the Moreau envelope by Attouch and Wets providesarXiv:2006.08667v3 fatcat:6tjb5cr4njhkdddwwclhtme7ha