# Last-Iterate Convergence of Anchored Gradient Descent

arXiv: https://arxiv.org/abs/2604.12235 · HTML: https://mlsanity.com/paper/2604.12235/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2026.

## Built on by (most cited first, 3 of 3)

- [Advancing Mathematics Research with AI-Driven Formal Proof Search](https://mlsanity.com/paper/2605.22763/) (2026)
- [A Unifying View of Anchoring via Operator-Side Tikhonov Regularization](https://mlsanity.com/paper/2605.30905/) (2026)
- [Improving the Last-Iterate Guarantees of Anytime Algorithms for Stochastic Monotone Variational Inequalities](https://mlsanity.com/paper/2609.15257/) (2026)

## Abstract (arXiv)

We study the monotone inclusion problem 0∈ F(z)+A(z), where F is monotone and Lipschitz, and A is maximally monotone, a framework that encompasses monotone variational inequalities and convex-concave saddle-point problems with constraints or regularization. It is well known that vanilla gradient descent diverges for this problem, whereas optimism-based methods such as Extragradient and accelerated methods that combine both optimism and anchoring, such as Extra Anchored Gradient, achieve last-iterate convergence. However, the anchoring-only method, anchored gradient descent, has been studied only in the unconstrained setting [RYY19, SST+26]. In this note, we extend the anchored gradient descent method to the monotone inclusion problem and prove a last-iterate convergence rate of O(1/√T) in terms of the tangent residual. We build on the recent proof in the unconstrained setting [SST+26] and use techniques from [COZ24] to extend it to the general inclusion setting.