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<p>This paper introduces new Conjugate Gradient methods designed to enhance neural network training and solve unconstrained optimization problems. These new algorithms are built from existing Conjugate Gradient frameworks through the addition of new conjugacy parameters and approximations derived using Taylor series expansion. These algorithms are contrasted with the popular Dai-Yuan algorithm on both unconstrained optimization problems and in training neural networks. Numerical simulations demonstrate that the new algorithms outperform the famous algorithms in both efficiency and precision, yielding superior results with fewer iterations and smaller mean squared errors. The new algorithms are rigorously studied for global convergence under strong Wolfe conditions and display impressive improvements in efficiency and robustness. This research makes a valuable contribution to gradient-based optimization of neural network training, exemplifying the strength of such emerging methods in resolving highly complicated optimization challenges in Artificial Intelligence and, in large part, machine learning-based applications.</p>

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Efficient conjugate gradient methods for unconstrained optimization and neural network applications

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Basim A. Hassan,
  • Issam A. R. Moghrabi,
  • Alaa Luqman Ibrahim,
  • Nivine Guler,
  • Hawraz N. Jabbar

摘要

This paper introduces new Conjugate Gradient methods designed to enhance neural network training and solve unconstrained optimization problems. These new algorithms are built from existing Conjugate Gradient frameworks through the addition of new conjugacy parameters and approximations derived using Taylor series expansion. These algorithms are contrasted with the popular Dai-Yuan algorithm on both unconstrained optimization problems and in training neural networks. Numerical simulations demonstrate that the new algorithms outperform the famous algorithms in both efficiency and precision, yielding superior results with fewer iterations and smaller mean squared errors. The new algorithms are rigorously studied for global convergence under strong Wolfe conditions and display impressive improvements in efficiency and robustness. This research makes a valuable contribution to gradient-based optimization of neural network training, exemplifying the strength of such emerging methods in resolving highly complicated optimization challenges in Artificial Intelligence and, in large part, machine learning-based applications.