A comparison of spectral conjugate gradient coefficients for unconstrained optimization

Conjugate gradient (CG) methods are among the most effective techniques for solving nonlinear optimization problems. Recently, a lot of research for modification and improvement of CG methods has been made. There are a few types of CG methods such as classical, spectral, hybrid, and three-term methods. The spectral CG method is shown to outperform other CG methods in past studies, where it was developed to improve the CG method's efficiency in terms of CPU time and iteration numbers. Consequently, the efficiency of three spectral CG methods—sSMARZ, SRMIL, and SCD from previous studies in solving test problems is observed in this study. The objectives of this study are to show that the selected spectral CG methods satisfy sufficient descent conditions and to determine the efficiency of the selected spectral CG methods in exact line search in solving certain standard optimization functions. The methodology of this research is conducted in four phases: literature phase, selection of three spectral CG methods, theoretical phase, and numerical phase. Conclusively, according to numerical results, the sSMARZ approach is superior and more effective than methods SRMIL and SCD.