# Inertial Krasnoselskii-Mann Iterations

arXiv: https://arxiv.org/abs/2210.03791 · HTML: https://mlsanity.com/paper/2210.03791/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2022.

## Built on by (most cited first, 5 of 5)

- [Gradient-free Decoder Inversion in Latent Diffusion Models](https://mlsanity.com/paper/2409.18442/) (2024)
- [Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis](https://mlsanity.com/paper/2501.10806/) (2025)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [Inertial Quadratic Majorization Minimization with Application to Kernel Regularized Learning](https://mlsanity.com/paper/2507.04247/) (2025)
- [Stochastic Inertial Krasnosel'skii-Mann Iteration Achieves Near-Optimal Sample Complexity](https://mlsanity.com/paper/2609.28543/) (2026)

## Abstract (arXiv)

We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and show that passing from one regime to the other is a continuous process in terms of the hypotheses on the parameters. Numerical illustrations are provided for an inertial primal-dual method and an inertial three-operator splitting algorithm, whose performance is superior to that of their non-inertial counterparts.