Convergence analysis of a new relaxed algorithm with inertial for solving split feasibility problems. (English) Zbl 07884565
Summary: In this paper, we introduce a new algorithm for solving split feasibility problems in Hilbert spaces. The algorithm stems from the relaxed CQ method and the alternated inertial step method. The proposed algorithm uses variable step-sizes which are updated at each iteration by a cheap computation without linesearch. This step-size rule allows the resulting algorithm to work more easily without the prior knowledge of the operator norm. Numerical experiments are implemented to illustrate the theoretical results and also to compare with existing algorithms.
MSC:
| 49J53 | Set-valued and variational analysis |
| 65K10 | Numerical optimization and variational techniques |
| 49M37 | Numerical methods based on nonlinear programming |
| 90C25 | Convex programming |
| 47H10 | Fixed-point theorems |
Keywords:
split feasibility problems; relaxed CQ-algorithms; alternated inertial method; fixed point; bounded linear operator; Hilbert spaceSoftware:
iPiascoReferences:
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