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
A novel method is proposed that achieves a new upper bound of $\tilde{\mathcal{O}}(m+ m+ m^{1/7} \epsilon^{-2/7})$ and significantly improves the prior one (Chen, Liu, Luo, and Zhang, COLT 2026), which significantly improves the prior one.
Xin-Liang Zhang, Le-Si Chen, Chengchang Liu et al.· 2 citations
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
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
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