- Title
- An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator
- Creator
- Dao, Minh; Phan, Hung
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/180580
- Identifier
- vital:15766
- Identifier
-
https://doi.org/10.1186/s13663-021-00701-8
- Identifier
- ISBN:1687-1820 (ISSN)
- Abstract
- Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators are generalized monotone and their resolvents are computable, while the other operator is cocoercive but its resolvent is missing or costly to compute. Our splitting algorithm adapts new parameters to the generalized monotonicity of the operators and, at the same time, combines appropriate forward and backward steps to guarantee convergence to a solution of the problem. © 2021, The Author(s).
- Publisher
- Springer Nature
- Relation
- Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (2021), p.
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- http://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright @ The Author(s) 2021
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; 0102 Applied Mathematics; Conically averaged operator; Fixed point iterations; Forward-backward algorithm; Three-operator splitting
- Full Text
- Reviewed
- Funder
- MND was partially supported by the Federation University Australia under Grant RGS21-8. HMP was partially supported by Autodesk, Inc. via a gift made to the Department of Mathematical Sciences, UMass Lowell.
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