{"ID":23475262,"CreatedAt":"2026-09-18T01:09:05.407443952Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20327","arxiv_id":"2609.20327","title":"Near-Optimal Pure Single-Loop Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization","abstract":"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.","short_abstract":"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 metho...","url_abs":"https://arxiv.org/abs/2609.20327","url_pdf":"https://arxiv.org/pdf/2609.20327v1","authors":"[\"Minhao Zhang\",\"Zi Xu\"]","published":"2026-09-17T13:02:58Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}