Abstract
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.
Highlights
The spectral Conjugate gradient (CG) methods are among the most efficient variant of CG methods designed to solve large-scale problems
We proposed some spectral CG methods using the classical CG search direction
This paper focuses on the application of the spectral CG methods for unconstrained optimization
Summary
The spectral CG methods are among the most efficient variant of CG methods designed to solve large-scale problems. Application of spectral conjugate gradient methods for solving unconstrained optimization problems 199 uncertain [12]. The strategy of fitting the best line through the data would minimize the sum of the residual error squares for the data available. This problem is similar to the minimization problem in unconstrained optimization [17]. We employ the spectral PRP and WYL CG parameter to obtain the solution of the given unconstrained optimization problem. Recall that the orthogonality of gradients gkTgk−1 = 0 and φk and ∅k are the new spectral parameters computed by exact line search procedure.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
