Solving unconstrained optimization problems using modified conjugate gradient parameter with sufficient descent condition - Kamilu Uba Kamfa
Conjugate gradient (CG) methods are used for solving unconstrained optimization problem. Recently, various studies and modifications have been carrying out to improve these methods. This study proposed a new modification of Hestenes and Steifel (HS) parameter for solving unconstrained optimization problem using exact line searches. The modification is motivated by Hestenes and Steife1 formula, where the denominator is change while holding the numerator. This modified parameter fJk has been tested using seventeen standard optimization test problems utilizing MATLAB 7.10.0 subroutine programming and the outcome is recorded. The performance of this newly parameter based on the and the number of iteration and CPU time is compared with the performance of other CG parameters which include Fletcher and Reeves (FR , Polak, Ribiere and Polyak (pRP), Abdelrhaman, Mustafa, Rivaie and Ismail (AMRI) method. In fact, for each test problems four different initial points is considered ranges from the one near to the solution point to one further away. The numerical results have shown that this modified parameter performs better than FR, PRP and AMRI methods, while it holds its simplicity and possesses the global convergence properties.