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

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
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.

scholarly journals A New Nonlinear Conjugate Gradient Method Based on the Scaled Matrix

2017 ◽  
Vol 27 (5) ◽  
pp. 68
Author(s):  
Basim A. Hassan ◽  
Haneen A. Alashoor
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Results ◽  
New Method ◽  
Test Problems ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
New Type ◽  
The Given

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.

scholarly journals A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
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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