Author

Lesi Chen

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Preprint Sep 2026

Optimal High-Order Methods for Solving Monotone Variational Inequalities

We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI). Monteiro and Svaiter (SIAM J. Optim., 2012) showed that a second-order method, NPE, converges at a rate of $\mathcal{O}(T^{-1.5})$. For convex-concave minimax optimization, a subclass of MVI problems, Chen, Liu, Luo, a...

Xin-Liang Zhang, Le-Si Chen, Lin-Xuan Pan et al. · 1 citation

Preprint Aug 2026

Halpern Iteration Achieves $\tilde{\mathcal{O}}(\epsilon^{-1/p})$ $p$th-Order Oracle Complexity for Monotone Variational Inequalities

By using a large-step inexact Halpern iteration, a novel Halpern-NPE method is proposed that achieves an even faster rate of $\tilde{\mathcal{O}}(T^{-2})$ for solving MVIs and improves all prior results for $p \ge 2$ and matches the classical extragradient method for p=1.

Le-Si Chen, Xin-Liang Zhang, He Wang et al. · 0 citations

Preprint Jul 2026

Optimal Convex Optimization with Inexact Second-Order Oracles

This paper shows that AINE can find an $\epsilon$-solution in the inexact second-order oracle (ISO) complexity of $\delta/\epsilon)^{1/2} + (L_2/\epsilon)^{2/7} )$ when the Hessian is $L_2$-Lipschitz continuous, and establishes matching oracle complexity lower bounds for both setups.

Lesi Chen, Chengchang Liu, Luo Luo et al. · 1 citation