A new kind of conjugate gradient methods for unconstrained optimization - Rabi'u Bashir Yunus
Conjugate gradient (CG) algorithms have been broadly applied to solve large-scale unconstrained optimization problems, because of its robustness, low memory requirement, and global convergence properties. Numerous studies and modifications have been carried out recently to improve these methods. In this research, a new modification of CG coefficient (f3k) is proposed in order to solve unconstrained optimization problems using the exact line searches. The idea of the modification is motivated based on the formula of Rivaie, Abdelrhaman, Mustafa and Ismail (RAMI) method. The new proposed f3k has been tested upon nineteen standard optimization test problems using MATLAB version 7.6.0 (R2008a) subroutine programming. The new proposed f3k is compared in terms of number of iteration and CPU time with other two classical formula of Fletcher and Reeves (FR), Polak, Ribiere and Polyak (PRP) and recent version of CG RAMI method. For every problems, four different initial points have been considered, ranging from the nearby, to the one that is far away from the solution point. The numerical results have clearly shown that this new proposed formula performs better than the FR, PRP and RAMI method. It also maintains its simplicity and possesses sufficient descent condition and global convergence properties.