| Summary: | Conjugate gradient (CG) method is the well-known method for solving unconstrained problems. The CG methods have many advantages such as its simple algorithm , low memory storage ad global convergence properties. In this research , a new spectral CG is proposed by modifying Rivaie-Mustafa -Ismail-Leong (RMIL) method. This new method is known as Spectral RMIL (SRMIL). Using inexact Strong Wolfe line search, this new spectral CG is compared with some famous classical CG coefficient such as RMIL, Polak and Ribiere (PR) and Conjugate Descent (CD) methods. Different set of variables have been chosen to be tested with fifteen standard test problems utilizing matlabR2012 subroutine programming. Four different initial points have been used for each standard test problems in order to show the efficiency of this method. The initial points have been from the one that is closer to the minimum point and to the one that is further away from the minimum point. The percentages of comparisons based on the iteration number show 96.43% ( SRMIL) and SCD), 93.59 % ( SRMIL and CD), 85.00 % (SRMIL and RMIL) and 77.14 % ( SRMIL and PR ). Meanwhile the percentages of comparisons for central Processing Unit ( CPU) times show 92.14 % ( SRMIL an PR ). Thus, this new method outperforms the other CG methods. Besides, numerical results based on the iteration number and CPU time also show that this new proposed method possessed global convergence properties.
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