The Strong Convergence of Douglas-Rachford Methods for the Split Feasibility Problem

Qiao-Li Dong (), Lulu Liu and Themistocles M. Rassias ()
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Qiao-Li Dong: College of Science, Civil Aviation University of China
Lulu Liu: College of Science, Civil Aviation University of China
Themistocles M. Rassias: National Technical University of Athens

A chapter in Mathematical Analysis in Interdisciplinary Research, 2021, pp 213-233 from Springer

Abstract: Abstract In this article, we introduce several Douglas-Rachford method to solve the split feasibility problems (SFP). Firstly, we propose a new iterative method by combining Douglas-Rachford method and Halpern iteration. The stepsize is determined dynamically which does not need any prior information about the operator norm. A relaxed version is presented for the SFP where the two closed convex sets are both level sets of convex functions. The strong convergence of two proposed methods is established under standard assumptions. We also propose an iterative method by combining Douglas-Rachford method with Haugazeau algorithm, and show its strong convergence. The numerical examples are presented to illustrate the advantage of our methods by comparing with other methods.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84721-0_12

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DOI: 10.1007/978-3-030-84721-0_12

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