Comparison between four non-classical conjugate gradient method for solving unconstrained optimization problem / Nik Nurshahfini Daud and Farah Ellyna Mohamad Fadzal

Conjugate gradient method is an efficient technique to solve unconstrained optimization problem. This method was proposed by Magnus Hestenes and Eduard Stiefel in 1952. For our research, it focus on non-classical which is Fletcher-Reeves (FR) and PRP for hybrid conjugate gradient, modified, scaled and parametrized methods. Hybrid conjugate gradient is the combination of attractive features of known conjugate gradient such as PRP and FR. Modified is where the existing numerator and denominator is modified with new terms. Scaled is when a parameter is added at search direction. Parametrized is added a parameter to a classical conjugate gradient. To find the best method, we compare the methods in terms of its efficiency and robustness. Efficiency is measured by the number of iteration and CPU time. Whereas, robustness is the ability of method to solve the most problems or test function than other methods. As a conclusion, from this study, we could determine what are the factors could make PRP-FR Hybrid, Scaled, Modified and Parametrized methods more efficient and more robust.