<p>The Hestenes-Stiefe (HS) conjugate gradient method is very effective in resolving larger-scale sophisticated smoothing optimization tasks due to its low computational requirements and high computational efficiency. Additionally, the algorithm has been employed in practical applications to address image restoration and machine learning issues. In this paper, the authors proposed an improved Hestenes-Stiefe conjugate gradient algorithm having characteristics like: ⅰ) The algorithm depicts the decreasing fea…