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In this work, we study the computational complexity of reducing the squaredgradient magnitude for smooth minimax optimization problems. First, we presentalgorithms with accelerated $\mathcal{O}(1/k^2)$ last-iterate rates, fasterthan the existing $\mathcal{O}(1/k)$ or slower rates for extragradient, Popov,and gradient descent with anchoring. The acceleration mechanism combinesextragradient steps with anchoring and is distinct from Nesterov'sacceleration. We then establish optimality of the $ \mathcal{O}(1/k^2)$ ratethrough a matching lower bound.

Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with $\mathcal{O}(1/k^2)$ Rate on Squared Gradient Norm