Solving monotone inclusions via compositions of nonexpansive averaged operators. (English) Zbl 1153.47305
Summary: A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators. The analysis covers proximal methods for common zero problems as well as for various splitting methods for finding a zero of the sum of monotone operators.
MSC:
| 47H10 | Fixed-point theorems |
| 47H05 | Monotone operators and generalizations |
| 47N20 | Applications of operator theory to differential and integral equations |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
Averaged operator; Douglas-Rachford method; Forward-backward method; Monotone inclusion; Monotone operator; Proximal point algorithmReferences:
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