# Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces

arXiv: https://arxiv.org/abs/1301.4506 · HTML: https://mlsanity.com/paper/1301.4506/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2013.

## Built on by (most cited first, 4 of 4)

- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression](https://mlsanity.com/paper/2105.13271/) (2021)
- [LPC-SM: Local Predictive Coding and Sparse Memory for Long-Context Language Modeling](https://mlsanity.com/paper/2604.03263/) (2026)

## Abstract (arXiv)

We model a problem motivated by road design as a feasibility problem. Projections onto the constraint sets are obtained, and projection methods for solving the feasibility problem are studied. We present results of numerical experiments which demonstrate the efficacy of projection methods even for challenging nonconvex problems.