Abdellatif Moudafi, Byrne’s extended CQ-algorithms in the light of Moreau-Yosida regularization
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DOI: 10.23952/asvao.3.2021.1.03
Volume 3, Issue 1, 30 April 2021, Pages 21-26
Abstract. Given a real matrix
, a maximal monotone operator
and a maximal monotone operator
the split feasibility null-point problem is to find
satisfying
with
Based on a regularization point of view of a Byrne’s idea, by replacing the operators by their Yosida approximates, we propose to consider the problem of finding
such that
and then to introduce the following extended CQ-Algorithm
where and
with
being the largest eigenvalue of
. In the context of split feasibility problems, this clearly reduces to Byrne’s extended CQ-algorithm, namely,
where
and
are the orthogonal projections onto the nonempty closed convex sets
and
, respectively.
How to Cite this Article:
Abdellatif Moudafi, Byrne’s extended CQ-algorithms in the light of Moreau-Yosida regularization, Appl. Set-Valued Anal. Optim. 3 (2021), 21-26.