Conjugated Gradient with Four Terms for Nonlinear Unconstrained Optimization

Abstract

The nonlinear conjugate gradient (GJG) technique is an effective tool for addressing minimization on a huge scale. It can be used in a variety of applications., We presented a novel conjugate gradient approach based on two hypotheses, and we equalized the two hypotheses and retrieved the good parameter in this article. To get a new conjugated gradient, we multiplied the new parameter by a control parameter and substituted it in the second equation. a fresh equation for 𝛽𝑘 is proposed. It has global convergence qualities. When compared to the two most common conjugate gradient techniques, our algorithm outperforms them in terms of both the number of iterations (NOIS) and the number of functions (NOFS). The new technique is efficient in real computing and superior to previous comparable approaches in many instances, according to numerical results.