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Abstract and Applied Analysis
Volume 2013, Article ID 780107, 5 pages
Research Article

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

1College of Mathematics, Qingdao University, Qingdao 266071, China
2School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 8 March 2013; Accepted 25 March 2013

Academic Editor: Yisheng Song

Copyright © 2013 Yuan-yuan Chen and Shou-qiang Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.