Journal Article10.1007/S11590-011-0324-0
Conjugate gradient methods using value of objective function for unconstrained optimization
Hideaki Iiduka,Yasushi Narushima +1 more
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TL;DR: This paper proposes two nonlinear conjugate gradient methods which take into account mostly information about the objective function and proves that they converge globally and numerically compare them with conventional methods.
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Abstract: Conjugate gradient methods have been widely used as schemes to solve large-scale unconstrained optimization problems. The search directions for the conventional methods are defined by using the gradient of the objective function. This paper proposes two nonlinear conjugate gradient methods which take into account mostly information about the objective function. We prove that they converge globally and numerically compare them with conventional methods. The results show that with slight modification to the direction, one of our methods performs as well as the best conventional method employing the Hestenes–Stiefel formula.
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Citations
A new formula for conjugate parameter computation based on the quadratic model
TL;DR: In this article, a new formula of conjugate gradient methods based on the quadratic model was derived, which has the most excellent performance contrast to the other standard CG methods.
Two-versions of descent conjugate gradient methods for large-scale unconstrained optimization
Hawraz N. Jabbar,Basim A. Hassan +1 more
TL;DR: A Hessian approximation in a diagonal matrix form on the basis of second and third-order Taylor series expansion was employed in this study and the sufficient descent property for the proposed algorithm are proved.
A new type of descent conjugate gradient method with exact line search
Nurul Hajar,Mustafa Mamat,Mohd Rivaie,Ibrahim Jusoh +3 more
- 02 Jun 2016
TL;DR: This new CG method satisfies descent condition and its global convergence is established using exact line search and it substantially outperforms the previous CG methods.
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A combination of Polak-Ribiere and Hestenes-Steifel coefficient in conjugate gradient method for unconstrained optimization
TL;DR: Numerical result show that this new CG method based on combination of two classical CG methods is quite effective when measured based on number of iteration and CPU times.
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TL;DR: This paper presents a new version of the conjugate gradient method, which converges globally, provided the line search satisfies the standard Wolfe conditions.
1.3K