The new search direction of four term conjugate gradient method for unconstrained optimization

Abstract

In this paper, we suggested a new four-term CG method, by expanding the three-term CG method to the four-term CG method. The search direction p, with some newly proposed parameters, is a four-term hybrid form for modified traditional CG methods. This hybridization yielded a newly created hybrid CG method with four terms as its ultimate result. The new method proposed ( the four-term CG method ) fulfills the conjugacy condition by the Dai-Laiao method and possesses sufficient descent property. Also, it was confirmed that the suggested new method would globally converge to the general Wolfe conditions beneath an adequate assumption. Finally, a comparison was made between the three terms CG that were adopted in the expansion and the proposed four-term formula, the computational results demonstrated the new method's robustness and effectiveness.