Exploring Enhanced Conjugate Gradient Methods: A Novel Family of Techniques for Efficient Unconstrained Minimization

Given that the conjugate gradient method (CGM) is computationally efficient and user-friendly, it is often used to address large-scale, unconstrained minimization issues. Numerous researchers have created new conjugate gradient (CG) update parameters by modifying the initial set, also referred to as classical CGMs. This has resulted in the development of several hybrid approaches. This work's major goal is to create a new family of techniques that can be used to create even more new methods. Consequently, Hestenes-Stiefel's update parameter and a new family involving Polak-Ribiere-Polyak and Liu-Storey CGMs are considered. By changing the parameters of this CGM family, a novel approach that possesses sufficient descent characteristics is obtained. A numerical experiment including many unconstrained minimization problems (UMP) is carried out to assess the novel method's efficacy compared to existing approaches. The result reveals that the new CG approach performs better than the current ones.