Performance of a New Hybrid Conjugate Gradient Method

Currently, many modifications have been made to the conjugate gradient (CG) method. One approach is to hybridize the method. The CG method proposed in this paper is in the form of hybrids, and the performance was evaluated under two different line searches: exact and inexact. HSMR, a proposed hybrid CG, is formed after combining two CG methods, which are the RMIL and SMR methods. Twenty-one different test functions were used to compare the two functions under different dimensions. A comparison is made by counting the difference in iterations numbers and the total amount of CPU time for both line searches. Comparison results showed that the hybrid CGs under exact line search outperformed the inexact line searches as to the core process’s CPU time and overall iteration count.