An alternative formula for conjugate gradient coefficient with descent properties for unconstrained optimization - Ibrahim Sulaiman Mohammed
Conjugate gradient method (CG) plays a crucial role in unconstrained optimization. Numerous research and modifications have been done recently to improve these methods efficiency. In this research, a new formula for CG coefficient Cf3k) is proposed for solving unconstrained optimization problems using exact line searches. This new (f3k) has been tested based on twenty one standard optimization test problems using MATLAB version 7.6.0 (R 2008a) subroutine programing to check its efficiency and robustness. The new formula is compared with well-known CG formulas of Fletcher and Reeves (FR), Polak, Ribiere and Polyak (PRP) and a recent version of CG by Abdelrhaman, Mustafa, Rivaie, and Ismail (AMRI) methods. For every test problem, four different initial points are used ranging from points closer to the solution points, and moving on to the points that are further away. The numerical results based on number of iterations and CPU time are analysed using the performance profile introduced by Dolan and More. The result shows that this new version of CG formula outperforms the performance of FR, PR and AMRI methods in terms of number of iterations and CPU time, while still retaining its simplicity. It is also shown that this method possesses global convergence properties.