The Numerical Calculation of Hybrid Conjugate Gradient Method Under Armijo Line Search and Its Application
Conjugate gradient (CG) method is known due to its simplicity, global convergence and low memory requirement. To date, the research on CG method in Google Scholar has reached 1470000. Nowadays, the modification on hybrid CG method has become a focus among researchers. Thus, this paper introduces a new hybrid CG coefficient by combining two previous coefficients, Linda-Aini-Mustafa-Rivaie (LAMR) and Norrlaili-Rivaie-Mustafa-Ismail (NRMI). Since LAMR has a good performance under strongWolfe while NRMI is quite good with exact line search, it is guaranteed that the new proposed hybrid CG method, NL will yield a good numerical analysis under Armijo line search. NL is compared to LAMR, NRMI and Abashar-Mustafa-Rivaie-Ismail (AMRI) to solve the unconstrained optimization problems. Based on the performance profile, NL coefficient is able to solve 58% problems with least iteration number and 52% problems with least CPU time. In order to test its capability, this NL coefficient is applied in regression analysis for data fitting. A real data set concerning Employees’ Provident Fund (EPF) dividend rate has been chosen to construct the linear regression model. The linear model of NL coefficient is compared to the least square and Excel trendline methods. According to the relative error, it shows that NL coefficient is applicable to solve real-life problem which makes it a promising method.