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Minimax problems, such as generative adversarial network, adversarialtraining, and fair training, are widely solved by a multi-step gradient descentascent (MGDA) method in practice. However, its convergence guarantee islimited. In this paper, inspired by the primal-dual hybrid gradient method, wepropose a new semi-anchoring (SA) technique for the MGDA method. This makes theMGDA method find a stationary point of a structured nonconvex-nonconcavecomposite minimax problem; its saddle-subdifferential operator satisfies theweak Minty variational inequality condition. The resulting method, namedSA-MGDA, is built upon a Bregman proximal point method. We further develop itsbacktracking line-search version, and its non-Euclidean version for smoothadaptable functions. Numerical experiments, including a fair classificationtraining, are provided.

Semi-Anchored Multi-Step Gradient Descent Ascent Method for Structured Nonconvex-Nonconcave Composite Minimax Problems