Abstract and Applied Analysis

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

Yuan-yuan Chen and Shou-qiang Du

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 780107, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393444400

Digital Object Identifier
doi:10.1155/2013/780107

Mathematical Reviews number (MathSciNet)
MR3044994

Zentralblatt MATH identifier
1278.90400

Citation

Chen, Yuan-yuan; Du, Shou-qiang. A New Smoothing Nonlinear Conjugate Gradient Method for Nonsmooth Equations with Finitely Many Maximum Functions. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 780107, 5 pages. doi:10.1155/2013/780107. https://projecteuclid.org/euclid.aaa/1393444400


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