An Approximation Technique for General Split Feasibility Problems Based on Projection onto the Intersection of Half-spaces

Authors

  • Guash Haile Taddele Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, P.O. Box 445, Debre Berhan, Ethiopia https://orcid.org/0000-0002-5954-7321
  • Songpon Sriwongsa Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) https://orcid.org/0000-0002-5137-8113

DOI:

https://doi.org/10.58715/ncao.2023.2.1

Keywords:

Split feasibility problem, Self-adaptive technique, Half-space relaxation, Strong convergence

Abstract

This paper presents a novel relaxed CQ algorithm for solving the multiple-sets split feasibility problem with multiple output sets (MSSFPMOS) in infinite-dimensional real Hilbert spaces. The proposed method replaces the projection to half-space with the projection to the intersection of two half-spaces, resulting in accelerated convergence by utilizing previous half-spaces. The present study introduces a novel algorithm that dynamically determines the stepsize, without any a priori knowledge of the operator norm required. Furthermore, the algorithm is proven to exhibit strong convergence to the minimum-norm solution of the MSSFPMOS. Finally, a number of numerical experiments have been conducted to showcase the impressive performance of the proposed algorithm.

Author Biographies

Guash Haile Taddele, Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, P.O. Box 445, Debre Berhan, Ethiopia

Assistant Professor in Mathematics at Xiamen University Malaysia. 

Songpon Sriwongsa, Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT)

Assistant Professor in Mathematics at King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand

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Published

2023-06-30

How to Cite

Taddele, G. H., & Sriwongsa, S. (2023). An Approximation Technique for General Split Feasibility Problems Based on Projection onto the Intersection of Half-spaces. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 2(1), 1–29. https://doi.org/10.58715/ncao.2023.2.1

Issue

Vol. 2 No. 1 (2023): January - June, 2023

Section

Articles

License

Copyright (c) 2023 Guash Haile Taddele, Songpon Sriwongsa

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