Application of spectral conjugate gradient methods for solving unconstrained optimization problems

Conjugate gradient (CG) methods are among the most efficient numerical methods for solving unconstrained optimization problems. This is due to their simplicty and less computational cost in solving large-scale nonlinear problems. In this paper, we proposed some spectral CG methods using the classical CG search direction. The proposed methods are applied to real-life problems in regression analysis. Their convergence proof was establised under exact line search. Numerical results has shown that the proposed methods are efficient and promising.