  Minimax problems, such as generative adversarial network, adversarial
training, and fair training, are widely solved by a multi-step gradient descent
ascent (MGDA) method in practice. However, its convergence guarantee is
limited. In this paper, inspired by the primal-dual hybrid gradient method, we
propose a new semi-anchoring (SA) technique for the MGDA method. This makes the
MGDA method find a stationary point of a structured nonconvex-nonconcave
composite minimax problem; its saddle-subdifferential operator satisfies the
weak Minty variational inequality condition. The resulting method, named
SA-MGDA, is built upon a Bregman proximal point method. We further develop its
backtracking line-search version, and its non-Euclidean version for smooth
adaptable functions. Numerical experiments, including a fair classification
training, are provided.
