In this paper we study new algorithmic structures with Douglas-Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the string-averaging projections and into the block-iterative projection algorithmic structures, thereby creating new DR algorithmic schemes that include the recently proposed cyclic DR algorithm and the averaged DR algorithm as special cases. We further propose and investigate a new multiple-set-DR algorithmic operator. Convergence of all these algorithmic schemes is studied by using properties of strongly quasi-nonexpansive operators and firmly nonexpansive operators.
Bibliographical notePublisher Copyright:
© 2016 Society for Industrial and Applied Mathematics.
- Algorithmic structures
- Convex feasibility problem
- Firmly nonexpansive
- M-set-Douglas-Rachford operator
- Strictly Fejér monotone
- Strong convergence
ASJC Scopus subject areas
- Theoretical Computer Science