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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Yunus, Rabiu Bashir
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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A THREE-TERM CONJUGATE GRADIENT METHOD FOR LARGE-SCALE MINIMIZATION IN ARTIFICIAL NEURAL NETWORKS Omesa, Umar A; Waziri, Muhammad Y.; Moghrabi, Issam A. R.; Ibrahim, Sulaiman M.; E B, Gudu; S L, Fakai; Yunus, Rabiu Bashir; Madi, Elissa Nadia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1973-1988

Abstract

Conjugate Gradient (CG) methods are widely used for solving unconstrained optimization problems due to their efficiency and low memory requirements. However, standard CG methods may not always guarantee sufficient descent condition, which can impact their robustness and convergence behavior. Additionally, their effectiveness in training artificial neural networks (ANNs) remains an area of interest. In response, this paper presents a three-term conjugate gradient (CG) method for unconstrained optimization problems. The new parameter is formulated so that the search direction satisfies the sufficient descent condition. The global convergence result of the new algorithm is discussed under suitable assumptions. To evaluate the performance of the new method we considered some standard test problems for unconstrained optimization and applied the proposed method to train different ANNs on some benchmark data sets contained in the NN toolbox. The experimental results show that performance is encouraging for both unconstrained minimization test problems and in training neural networks.
AN IMPROVED HYBRID CONJUGATE GRADIENT METHOD WITH SPECTRAL STRATEGY AND ITS APPLICATIONS IN COVID-19 PREDICTION Kamfa, Kamilu; Yunus, Rabiu Bashir; Lawan, Muhammad Auwal
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2803-2814

Abstract

This paper introduces a hybrid conjugate gradient (CG) method for unconstrained optimization with a spectral strategy, inspired by key advancements in existing CG techniques. The proposed method guarantees a descent direction at every iteration, regardless of the line search scheme employed. Its global convergence is rigorously established under the Wolfe line search conditions. Numerical experiments on benchmark optimization problems demonstrate that the proposed method outperforms the FR and RMIL methods across multiple performance metrics. Furthermore, its effectiveness is showcased in a neural network framework for predicting chickenpox and COVID-19 infection cases, highlighting its practical applicability in real-world scenarios.
Co-Authors E B, Gudu Ibrahim, Sulaiman M. Kamfa, Kamilu Lawan, Muhammad Auwal Madi, Elissa Nadia Moghrabi, Issam A. R. Omesa, Umar A S L, Fakai Waziri, Muhammad Y.