# Universal Tensor Methods for Monotone Variational Inequalities

arXiv: https://arxiv.org/abs/2212.07824 · HTML: https://mlsanity.com/paper/2212.07824/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2022.

## Built on by (most cited first, 6 of 6)

- [Second-Order Min-Max Optimization with Lazy Hessians](https://mlsanity.com/paper/2410.09568/) (2024)
- [A Fully Parameter-Free Second-Order Algorithm for Convex-Concave Minimax Problems](https://mlsanity.com/paper/2407.03571/) (2024)
- [Multiple Greedy Quasi-Newton Methods for Saddle Point Problems](https://mlsanity.com/paper/2408.00241/) (2024)
- [Completely Parameter-Free Single-Loop Algorithms for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/2407.21372/) (2024)
- [Gradient Norm Regularization Second-Order Algorithms for Solving Nonconvex-Strongly Concave Minimax Problems](https://mlsanity.com/paper/2411.15769/) (2024)
- [Solving Convex-Concave Problems with tildeO(ε-4/7) Second-Order Oracle Complexity](https://mlsanity.com/paper/2506.08362/) (2025)

## Abstract (arXiv)

We study monotone variational inequalities whose operators have H"older continuous higher-order derivatives. For a fixed order p≥ 2, we assume that the (p-1)-th derivative of the monotone operator is H"older continuous with parameter nu∈[0,1] on a bounded closed convex set. We develop regularized tensor extragradient methods that combine a high-order Taylor approximation of the operator with an extragradient correction step. When the H"older parameter nu is known, our regularized tensor extragradient method finds an ε-weak solution using O(ε-2/(p+nu)) tensor-oracle calls. When nu is unknown, we propose a universal tensor extragradient method whose tensor-oracle complexity is O(ε-2p/((p+1)(p-1+nu))).