Minimax

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Period ending 2026-09-21

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Period ending 2026-09-14

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54 papers

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Date pendingHédi Hadiji, Sarah SachsImperfect-Information Games Equilibrium

Sep 17, 2026 · math.OCJ/K move · Enter open · S save

Near-Optimal Pure Single-Loop Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization

Minhao Zhang, Zi Xu

Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China

We study smooth strongly convex--strongly concave minimax optimization with general nonlinear coupling in the deterministic unconstrained setting. We propose a pure single-loop damped extragradient method with fixed parameters and two new full-gradient evaluations per iteration after one initialization query. The method uses an auxiliary feedback recursion and requires no inner solves, accuracy schedules, or staged restarts. We establish last-iterate linear convergence and show that reducing the squared Euclidean distance to the saddle point to an

\varepsilon

fraction of its initial value requires

O(\sqrt{κ_xκ_y}\log(2κ_xκ_y/\varepsilon))

full-gradient queries, where

κ_x=L/μ_x

and

κ_y=L/μ_y

. This bound attains the optimal condition-number order up to logarithmic factors through fixed explicit updates. Numerical experiments demonstrate the effectiveness of the method.

Convex Optimization Proximal Gradient Descent Minimax

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