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Convergence Analysis of a New Forward-Reflected-Backward Algorithm for Four Operators Without Cocoercivity.
- Source :
-
Journal of Optimization Theory & Applications . Aug2024, p1-29. - Publication Year :
- 2024
-
Abstract
- In this paper, we propose a new splitting algorithm to find the zero of a monotone inclusion problem that features the sum of three maximal monotone operators and a Lipschitz continuous monotone operator in Hilbert spaces. We prove that the sequence of iterates generated by our proposed splitting algorithm converges weakly to the zero of the considered inclusion problem under mild conditions on the iterative parameters. Several splitting algorithms in the literature are recovered as special cases of our proposed algorithm. Another interesting feature of our algorithm is that one forward evaluation of the Lipschitz continuous monotone operator is utilized at each iteration. Numerical results are given to support the theoretical analysis. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIPSCHITZ continuity
*HILBERT space
*MONOTONE operators
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 00223239
- Database :
- Academic Search Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 178760024
- Full Text :
- https://doi.org/10.1007/s10957-024-02501-7