# Gradient Projection Iterative Sketch for Large-Scale Constrained Least-Squares

arXiv: https://arxiv.org/abs/1609.09419 · HTML: https://mlsanity.com/paper/1609.09419/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2016.

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

- [Accelerating Plug-and-Play Image Reconstruction via Multi-Stage Sketched Gradients](https://mlsanity.com/paper/2203.07308/) (2022)
- [Equivariance Regularization for Image Reconstruction](https://mlsanity.com/paper/2202.05062/) (2022)
- [Operator Sketching for Deep Unrolling Networks](https://mlsanity.com/paper/2203.11156/) (2022)
- [Equivariant Test-Time Training with Operator Sketching for Imaging Inverse Problems](https://mlsanity.com/paper/2411.05771/) (2024)
- [Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models](https://mlsanity.com/paper/2509.06856/) (2025)

## Abstract (arXiv)

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence analysis for both proposed algorithms and demonstrate our methods' computational efficiency compared to classical accelerated gradient method, and the state of the art variance-reduced stochastic gradient methods through numerical experiments in various large synthetic/real data sets.