A new Dai-Liao-type algorithm for efficient neural network learning in medical diagnosis

Mehamdia Abd Elhamid; Raouf Ziadi; Alaa Luqman Ibrahim; Mohammed A. Saleh; Abdulgader Z. Almaymuni; Mehamdia Abd Elhamid; Raouf Ziadi; Alaa Luqman Ibrahim; Mohammed A. Saleh; Abdulgader Z. Almaymuni

doi:10.3934/math.2026771

AIMS Mathematics

2026, Volume 11, Issue 6: 18943-18969. doi: 10.3934/math.2026771

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A new Dai-Liao-type algorithm for efficient neural network learning in medical diagnosis

1.
University M'Hamed Bougara of Boumerdes, Boumerdes 35000, Algeria
2.
Laboratory of Fundamental and Numerical Mathematics (LMFN), Department of Mathematics, University Setif-1-Ferhat Abbas, Setif, Algeria
3.
Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistane Region, Iraq
4.
Department of Cybersecurity, College of Computer, Qassim University, Saudi Arabia

Received: 03 May 2026 Revised: 10 June 2026 Accepted: 22 June 2026 Published: 26 June 2026
MSC : 65K05, 90C30, 90C56

Conjugate gradient (CG) methods are considered among the most efficient methods for solving optimization problems thanks to their straightforward iterative process and low memory requirements. In the present work, we propose a combined CG method to address large-scale problems, with a particular application to training artificial neural networks (ANNs) for early breast cancer prediction and electrocardiogram (ECG) classification. Under the strong Wolfe line search conditions, the global convergence was demonstrated under mild assumptions and the generated descent direction and the convergence features of the suggested approach are examined. The proposed approach was successfully applied to train neural networks for early breast cancer prediction, achieving an accuracy of 98.24%, with precision, recall, and F1-score values of 0.99, 0.97, and 0.98, respectively. It also reduces the final mean squared error by over 52% and exhibited faster convergence with smoother training dynamics. Furthermore, on the ECG classification dataset, the proposed hybrid Dai-Liao (hDL$ ^{+} $) achieves an accuracy of 80.45%, demonstrating strong generalization performance across different medical diagnostic applications. Comparisons with recent CG methods on a set of test problems from the CUTE library confirmed the robustness and efficiency of the proposed method.
- optimization method,
- Dai-Liao method,
- artificial neural networks,
- breast cancer prediction,
- ECG classification,
- medical decision support systems
Citation: Mehamdia Abd Elhamid, Raouf Ziadi, Alaa Luqman Ibrahim, Mohammed A. Saleh, Abdulgader Z. Almaymuni. A new Dai-Liao-type algorithm for efficient neural network learning in medical diagnosis[J]. AIMS Mathematics, 2026, 11(6): 18943-18969. doi: 10.3934/math.2026771

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Abstract

Conjugate gradient (CG) methods are considered among the most efficient methods for solving optimization problems thanks to their straightforward iterative process and low memory requirements. In the present work, we propose a combined CG method to address large-scale problems, with a particular application to training artificial neural networks (ANNs) for early breast cancer prediction and electrocardiogram (ECG) classification. Under the strong Wolfe line search conditions, the global convergence was demonstrated under mild assumptions and the generated descent direction and the convergence features of the suggested approach are examined. The proposed approach was successfully applied to train neural networks for early breast cancer prediction, achieving an accuracy of 98.24%, with precision, recall, and F1-score values of 0.99, 0.97, and 0.98, respectively. It also reduces the final mean squared error by over 52% and exhibited faster convergence with smoother training dynamics. Furthermore, on the ECG classification dataset, the proposed hybrid Dai-Liao (hDL$ ^{+} $) achieves an accuracy of 80.45%, demonstrating strong generalization performance across different medical diagnostic applications. Comparisons with recent CG methods on a set of test problems from the CUTE library confirmed the robustness and efficiency of the proposed method.

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