New investigation Development of the Dai Yuan method for solving Unconstrained Optimization Problems

This paper proposes a novel parameter modification to the classical Dai-Yuan conjugate gradient (CG) method to enhance its efficiency in solving large-scale unconstrained optimization problems. The new approach maintains simplicity, low memory usage, and theoretical robustness, making it suitable for high-dimensional applications. A detailed theoretical analysis proves global convergence and descent properties under standard assumptions. Numerical experiments on benchmark problems demonstrate that the proposed method outperforms classical CG algorithms by delivering more accurate solutions with fewer iterations. These findings confirm the methods potential as an effective and reliable alternative, offering improved numerical stability and faster convergence for large-scale optimization tasks.