# Weak, Strong and Linear Convergence of the CQ-Method Via the Regularity of Landweber Operators

arXiv: https://arxiv.org/abs/1812.07450 · HTML: https://mlsanity.com/paper/1812.07450/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems](https://mlsanity.com/paper/2408.12100/) (2024)

## Abstract (arXiv)

We consider the split convex feasibility problem in a fixed point setting. Motivated by the well-known CQ-method of Byrne (2002), we define an abstract andweber transform which applies to more general operators than the metric projection. We call the result of this transform a Landweber operator. It turns out that the Landweber transform preserves many interesting properties. For example, the Landweber transform of a (quasi/firmly) nonexpansive mapping is again (quasi/firmly) nonexpansive. Moreover, the Landweber transform of a (weakly/linearly) regular mapping is again (weakly/linearly) regular. The preservation of regularity is important because it leads to (weak/linear) convergence of many CQ-type methods.