The modification conjugate coefficient for conjugate gradient method to solving unconstrained optimization problems

Abstract

In this manuscript, a novel conjugate coefficient is derived through the utilization of equality conjugate gradient direction in conjunction with a modified quasi-Newton (QN) direction. The demonstrated results establish that this innovative approach ensures both sufficient descent and global convergence, meeting the criteria of the Wolf line search condition and inexact line search. Through numerical experiments, we employ the proposed method on a diverse set of established test functions, clearly demonstrating its enhanced efficiency. A comparative analysis is conducted against the FR CG method using the Dolan-More performance profile based on the number of function evaluations (NOF), number of iterations (NOI), and CPU time.