Halpern Iteration Achieves $\tilde{\mathcal{O}}(ε^{-1/p})$ $p$th-Order Oracle Complexity for 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 the rate of $\mathcal{O}(T^{-1.5})$. For convex-concave minimax optimization, a subset of MVI problems, Chen, Liu, Luo, and Zhang (COLT 2025) recently improved the complexity to $\tilde{\mathcal{O}}( T^{-1.75})$ . However, it is open whether the conjectured complexity for MVI can be improved. In this paper, by using a large-step inexact Halpern iteration, we propose a novel Halpern-NPE method that achieves an even faster rate of $\tilde{\mathcal{O}}(T^{-2})$ for solving MVIs. We also provide t...
| Authors | Lesi Chen, Xinliang Zhang, Hengyu Wang et al. |
|---|---|
| Primary category | math.OC |
| Published | 9 August 2026 |
| Last updated at source | 9 August 2026 |
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