DOI: 10.24193/fpt-ro.2024.1.16

Authors: Ferdinard U. Ogbuisi, Yekini Shehu and Jen-Chih Yao

Abstract: 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.

Key Words and Phrases: Split feasibility problems, relaxed CQ-algorithms, alternated inertial method, fixed point, bounded linear operator, Hilbert space.

2010 Mathematics Subject Classification: 49J53, 65K10, 49M37, 90C25, 47H10.

Published on-line: February 1st, 2024.

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