scholarly journals A New Smoothing Conjugate Gradient Method for Solving Nonlinear Nonsmooth Complementarity Problems

Algorithms ◽  
2015 ◽  
Vol 8 (4) ◽  
pp. 1195-1209 ◽  
Author(s):  
Ajie Chu ◽  
Shouqiang Du ◽  
Yixiao Su
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Complementarity Problems

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.

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