# Accelerated Extragradient-Type Methods -- Part 2: Generalization and Sublinear Convergence Rates under Co-Hypomonotonicity

arXiv: https://arxiv.org/abs/2501.04585 · HTML: https://mlsanity.com/paper/2501.04585/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2025.

## Built on by (most cited first, 2 of 2)

- [RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolation](https://mlsanity.com/paper/2603.22155/) (2026)
- [A Unifying View of Anchoring via Operator-Side Tikhonov Regularization](https://mlsanity.com/paper/2605.30905/) (2026)

## Abstract (arXiv)

Following the first part of our project, this paper comprehensively studies two types of extragradient-based methods: anchored extragradient and Nesterov's accelerated extragradient for solving [non]linear inclusions (and, in particular, equations), primarily under the Lipschitz continuity and the co-hypomonotonicity assumptions. We unify and generalize a class of anchored extragradient methods for monotone inclusions to a wider range of schemes encompassing existing algorithms as special cases. We establish O(1/k) last-iterate convergence rates on the residual norm of the underlying mapping for this general framework and then specialize it to obtain convergence guarantees for specific instances, where k denotes the iteration counter. We extend our approach to a class of anchored Tseng's forward-backward-forward splitting methods to obtain a broader class of algorithms for solving co-hypomonotone inclusions. Again, we analyze O(1/k) last-iterate convergence rates for this general scheme and specialize it to obtain convergence results for existing and new variants. We generalize and unify Nesterov's accelerated extra-gradient method to a new class of algorithms that covers existing schemes as special instances while generating new variants. For these schemes, we can prove O(1/k) last-iterate convergence rates for the residual norm under co-hypomonotonicity, covering a class of nonmonotone problems. We propose another novel class of Nesterov's accelerated extragradient methods to solve inclusions. Interestingly, these algorithms achieve both O(1/k) and o(1/k) last-iterate convergence rates, and also the convergence of iterate sequences under co-hypomonotonicity and Lipschitz continuity. Finally, we provide a set of numerical experiments encompassing different scenarios to validate our algorithms and theoretical guarantees.