A Sufficient Descent 3-Term Conjugate Gradient Method for Unconstrained Optimization Algorithm

In recent years, 3-term conjugate gradient algorithms (TT-CG) have sparked interest for large scale unconstrained optimization algorithms due to appealing practical factors, such as simple computation, low memory requirement, better sufficient descent property, and strong global convergence property. In this study, minor changes were made to the BRB-CG method used for addressing the optimization algorithms discussed. Then, a new 3-term BRB-CG (MTTBRB) was presented. This new method solved large-scale unconstrained optimization problems. Despite the fact that the BRB algorithm achieved global convergence by employing a modified strong Wolfe line search, in this new MTTBRB-CG method the researchers employed the classical strong Wolfe-Powell condition (SWPC). This study also attempted to quantify how much better 3-term efficiency is than 2-term efficiency. As a result, in the numerical analysis, the new modification was compared to an effective 2-term CG- method. The numerical analysis demonstrated the effectiveness of the proposed method in solving optimization problems.