Mathematics and Statistics Vol. 9(6), pp. 882 - 888
DOI: 10.13189/ms.2021.090603
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A Modified Perry's Conjugate Gradient Method Based on Powell's Equation for Solving Large-Scale Unconstrained Optimization

Mardeen Sh. Taher ^1,*, Salah G. Shareef ^2
1 Department of Mathematics, College of Science, Duhok University, Kurdistan Region, Iraq
² Department of Mathematics, College of Science, Zakho University, Kurdistan Region, Iraq

ABSTRACT

It is known that the conjugate gradient method is still a popular method for many researchers who are focused in solving the large-scale unconstrained optimization problems and nonlinear equations because the method avoids the computation and storage of some matrices so the memory's requirements of the method are very small. In this work, a modified Perry conjugate gradient method which fulfills a global convergence with standard assumptions is shown and analyzed. The idea of new method is based on Perry method by using the equation which is founded via Powell in 1978. The weak Wolfe–Powell search conditions are used to choose the optimal line search, under the line search and suitable conditions, we prove both descent and sufficient descent conditions. In particular, numerical results show that the new conjugate gradient method is more effective and competitive when compared to other of standard conjugate gradient methods including: - CG- Hestenes and Stiefel (H/S) method, CG-Perry method, CG- Dai and Yuan (D/Y) method. The comparison is completed under a group of standard test problems with various dimensions from the CUTEst test library and the comparative performances of the methods are evaluated by total the number of iterations and the total number of function evaluations.

KEYWORDS
Conjugate Gradient, Wolfe Line Search, Descent and Sufficient Descent Conditions, Analysis of Convergence

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mardeen Sh. Taher , Salah G. Shareef , "A Modified Perry's Conjugate Gradient Method Based on Powell's Equation for Solving Large-Scale Unconstrained Optimization," Mathematics and Statistics, Vol. 9, No. 6, pp. 882 - 888, 2021. DOI: 10.13189/ms.2021.090603.

(b). APA Format:
Mardeen Sh. Taher , Salah G. Shareef (2021). A Modified Perry's Conjugate Gradient Method Based on Powell's Equation for Solving Large-Scale Unconstrained Optimization. Mathematics and Statistics, 9(6), 882 - 888. DOI: 10.13189/ms.2021.090603.