Weak, Strong and Linear Convergence of the CQ-Method Via the Regularity of Landweber Operators
Optimization and Control
2018-12-19 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1812.07450,
title = {Weak, Strong and Linear Convergence of the CQ-Method Via the Regularity of Landweber Operators},
author = {Andrzej Cegielski and Simeon Reich and Rafał Zalas},
journal= {arXiv preprint arXiv:1812.07450},
year = {2018}
}