# A learning-enhanced projection method for solving convex feasibility problems

## TL;DR

This paper introduces a generalized projection method for convex feasibility problems that learns from past projection steps to improve decision-making, with proven convergence and initial numerical results.

## Contribution

It presents a novel learning-enhanced projection algorithm that adapts based on previous steps, extending traditional cyclic projection methods.

## Key findings

- Proven convergence of the proposed algorithm.
- Initial numerical experiments demonstrate its effectiveness.
- The method adapts projections based on learned geometric information.

## Abstract

We propose a generalization of the method of cyclic projections, which uses the lengths of projection steps carried out in the past to learn about the geometry of the problem and decides on this basis which projections to carry out in the future. We prove the convergence of this algorithm and illustrate its behavior in a first numerical study.