A modification of spectral conjugate gradient method (MSM-2) for unconstrained optimization

The conjugate gradient approach for solving unconstrained optimization is gaining popularity among researchers due to its capacity to solve large-scale unconstrained optimization problems. The method is used for finding an optimum solution for nonlinear unconstrained optimization problems. Due to the upward trending in the conjugate gradient methods research, this research carried out a new spectral conjugate gradient method by combining the benefits of spectral conjugate gradient method and classical conjugate gradient methods. The Sri-Mustafa-2 (SM-2) method is combined with spectral conjugate gradient method namely as modified SM-2 or abbreviated as MSM-2. Theoretically, the proposed method needs to satisfy sufficient descent condition and global convergence properties. The MSM-2 method is then tested with 15 standard optimization test problems to retrieve the numerical result through MATLAB 2016b. The efficiency of the proposed method in terms of iteration number and CPU time is compared with other selected spectral CG method such as modified HS (MHS) and modified RMIL (MRMIL). Determine from numerical results, the MSM-2 is superior and most efficient method to solve unconstrained optimization problems than other selected spectral CG methods.