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arXiv · 1812.07450

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

Andrzej Cegielski·Simeon Reich·Rafał Zalas
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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.

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Andrzej Cegielski, Simeon Reich, Rafał Zalas. 2018-12-18. Weak, Strong and Linear Convergence of the CQ-Method Via the Regularity of Landweber Operators. https://arxiv.org/abs/1812.07450

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