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A generalized contraction proximal point algorithm with two monotone operators
- Source :
- Quaestiones Mathematicae; Vol 42, No 8 (2019); 1065-1078
- Publication Year :
- 2019
- Publisher :
- Taylor & Francis, 2019.
-
Abstract
- In this work, we introduce a generalized contraction proximal point algorithm and use it to approximate common zeros of maximal monotone operators A and B in a real Hilbert space setting. The algorithm is a two step procedure that alternates the resolvents of these operators and uses general assumptions on the parameters involved. For particular cases, these relaxed parameters improve the convergence rate of the algorithm. A strong convergence result associated with the algorithm is proved under mild conditions on the parameters. Our main result improves and extends several results in the literature.Mathematics Subject Classification (2010): 47J25, 47H05, 47H09.Keywords: Maximal monotone operator, contraction proximal point algorithm, alternating method, nonexpansive map, resolvent operator
- Subjects :
- Hilbert space
Monotonic function
Proximal point
symbols.namesake
Mathematics (miscellaneous)
Monotone polygon
Rate of convergence
Generalized contraction
Resolvent operator
symbols
Maximal monotone operator, contraction proximal point algorithm, alternating method, nonexpansive map, resolvent operator
Contraction (operator theory)
Algorithm
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 16073606 and 1727933X
- Database :
- OpenAIRE
- Journal :
- Quaestiones Mathematicae
- Accession number :
- edsair.doi.dedup.....79a7feefc2ad4b541b2054d9f9db210f