A New Nonlinear Conjugate Gradient Method Based on the Scaled Matrix

In this paper, a new type nonlinear conjugate gradient method based on the ScaleMatrix is derived. The new method has the decent and globally convergentproperties under some assumptions. Numerical results indicate the efficiency ofthis method to solve the given test problems.

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A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

Mathematical Problems in Engineering ◽

10.1155/2014/710376 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Shengwei Yao ◽

Xiwen Lu ◽

Bin Qin

Keyword(s):

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Large Scale ◽

Optimization Problems ◽

Special Role ◽

Conjugacy Condition ◽

Nonlinear Conjugate Gradient Method ◽

Nonlinear Conjugate Gradient ◽

The Given

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001). Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.

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A Hybrid Nonlinear Conjugate Gradient Method with Sufficient Descent Property

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.58-60.943 ◽

2011 ◽

Vol 58-60 ◽

pp. 943-949

Author(s):

Wan You Cheng ◽

Xue Jie Liu

Keyword(s):

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Numerical Experiments ◽

Test Problems ◽

Sufficient Descent Property ◽

Nonlinear Conjugate Gradient Method ◽

Descent Property ◽

Nonlinear Conjugate Gradient ◽

Sufficient Descent

In this paper, on the basis of the recently developed HZ (Hager-Zhang) method [SIAM J. Optim., 16 (2005), pp. 170-192], we propose a hybrid descent conjugate gradient method which reserves the sufficient descent property of the HZ method. Under suitable conditions, we prove the global convergence of the proposed method. Extensive numerical experiments show that the method is promising for the test problems from the CUTE library.

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A New Smoothing Nonlinear Conjugate Gradient Method for Nonsmooth Equations with Finitely Many Maximum Functions

Abstract and Applied Analysis ◽

10.1155/2013/780107 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Yuan-yuan Chen ◽

Shou-qiang Du

Keyword(s):

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Complementarity Problems ◽

Accumulation Point ◽

Merit Function ◽

New Method ◽

Nonsmooth Equations ◽

Nonlinear Conjugate Gradient Method ◽

Nonlinear Conjugate Gradient

The nonlinear conjugate gradient method is of particular importance for solving unconstrained optimization. Finitely many maximum functions is a kind of very useful nonsmooth equations, which is very useful in the study of complementarity problems, constrained nonlinear programming problems, and many problems in engineering and mechanics. Smoothing methods for solving nonsmooth equations, complementarity problems, and stochastic complementarity problems have been studied for decades. In this paper, we present a new smoothing nonlinear conjugate gradient method for nonsmooth equations with finitely many maximum functions. The new method also guarantees that any accumulation point of the iterative points sequence, which is generated by the new method, is a Clarke stationary point of the merit function for nonsmooth equations with finitely many maximum functions.

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A New Hybrid Conjugate Gradient Method with Guaranteed Descent for Unconstraint Optimization

Al-Mustansiriyah Journal of Science ◽

10.23851/mjs.v28i3.114 ◽

2018 ◽

Vol 28 (3) ◽

pp. 193 ◽

Cited By ~ 1

Author(s):

Basim A. Hassan

Keyword(s):

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Gradient Methods ◽

Test Problems ◽

Convergence Properties ◽

Nonlinear Conjugate Gradient ◽

Hybrid Conjugate Gradient Method ◽

Nonlinear Conjugate Gradient Methods ◽

The Given

The conjugate gradient method an efficient technique for solving the unconstrained optimization problem. In this paper, we propose a new hybrid nonlinear conjugate gradient methods, which have the descent at every iteration and globally convergence properties under certain conditions. The numerical results show that new hybrid method are efficient for the given test problems.

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