Strong Convergence Accelerated Alternated Inertial Relaxed Algorithm for Split Feasibilities with Applications in Breast Cancer Detection

Authors

  • Abdulwahab Ahmad Department of Mathematics, School of Secondary Education, Sciences, Federal College of Education, Katsina, Nigeria
  • Poom Kumam Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Fixed Point Research Laboratory, Room SCL 802, Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science , King Mongkut’s University of Technology Thonburi (KMUTT), Thailand

DOI:

https://doi.org/10.58715/bangmodjmcs.2025.11.6

Keywords:

Relaxed \(\mathcal{CQ}\) method, Alternated inertial method, Hybrid three-term conjugate gradient method, Split feasibility problem, Classification problem

Abstract

In this article, we construct an accelerated relaxed algorithm with an alternating inertial extrapolation step. The proposed algorithm uses a three-term conjugate gradient-like direction, which helps to fasten the sequence of its iterates to a point in a solution set. The algorithm employs a self-adaptive step-length criterion that does not require any information related to the norm of the operator or the use of a line-search procedure. Moreover, we formulate and prove a strong convergence theorem for the algorithm to a minimum-norm solution of a split feasibility problem in infinite-dimensional real Hilbert spaces. Furthermore, we investigate its applications in breast cancer detection by solving classification problems for an interesting real-world breast cancer dataset, based on the extreme learning machine (ELM) with the \(\ell_{1}\)-regularization approach (i.e., the Lasso model) and the \(\ell_{1}\)-\(\ell_{2}\) hybrid regularization technique. The performance results of the experiments demonstrate that the proposed algorithm is robust, efficient, and achieves better generalization performance and stability than some existing algorithms in the literature.

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Published

2025-04-30

How to Cite

Ahmad, A., & Kumam, P. (2025). Strong Convergence Accelerated Alternated Inertial Relaxed Algorithm for Split Feasibilities with Applications in Breast Cancer Detection. Bangmod International Journal of Mathematical and Computational Science, 11, 109–134. https://doi.org/10.58715/bangmodjmcs.2025.11.6

Issue

Section

Research Article