An Effective HS-CG Update: Avoiding Oscillations in Nonlinear Optimization

In this research, we introduce a modified direction update formula to improve the descent features of iterative optimization, therefore presenting a fresh approach to the Conjugate Gradient (CG) method. The proposed method adjusts the search direction at each iteration by incorporating gradient and step projections, weighted by inner products between gradient and step vectors. The modified HS-CG approach seeks to decrease the computational cost often associated with conventional approaches and speed up convergence by carefully balancing these projections. Experimental results demonstrate that our approach outperforms standard CG algorithms in achieving faster convergence on a range of benchmark problems, especially in high-dimensional spaces. This enhancement makes the method particularly promising for large-scale optimization challenges encountered in fields such as machine learning and engineering design.