Global convergence of a new class nonlinear conjugate gradient method with exact line search

Abstract

Unconstrained optimization is a widespread problem that can be solved by a mathematical technique known as the conjugate gradient method. This method is chosen because of its simplicity and less use of time in solving problems that can be seen when the result has less number of iteration with a faster time of the central processing unit (CPU). Motivated by this study, we are interested in researching as there are many modifications taking place in the conjugate gradient parameter. Therefore, in this study, five conjugate gradient parameters, including the preferred conjugate gradient parameter, modification of the Hestenes-Stiefel conjugate gradient parameter, will be analyzed. We focus on the problem of unconstrained optimization using the exact line search. The proof that this conjugate gradient parameter fulfilled the condition; global convergent condition under the exact line search will be shown. The performance of the conjugate gradient method with all conjugate gradient parameters was tested using 15 optimization test functions through MATLAB software to check whether the conjugate gradient method with the chosen conjugate gradient parameter could perform better and more efficiently than the conjugate gradient method with other conjugate gradient parameters based on the number of iterations and time. The conjugate gradient method’s accuracy and efficiency with each conjugate gradient parameter will be compared based on the percentage obtained in the cumulative frequency graph. The analysis shows that the conjugate gradient method’s performance with the chosen conjugate gradient parameter is more accurate and efficient than the conjugate gradient method with another conjugate gradient parameter.