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IMA Journal of Numerical Analysis Advance Access originally published online on November 14, 2008
IMA Journal of Numerical Analysis 2009 29(3):814-825; doi:10.1093/imanum/drn019
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A derivative-free nonmonotone line search and its application to the spectral residual method

Wanyou Cheng{dagger}

College of Software, Dongguan University of Technology, Dongguan 523000, China

Dong-Hui Li{ddagger}

College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

{dagger} Corresponding author. Email: chengwanyou421{at}yahoo.com.cn

{ddagger} Email: dhli{at}hnu.cn

Received on 31 May 2007. Revised on 23 February 2008.


  Abstract

In this paper we propose a derivative-free nonmonotone line search for solving large-scale nonlinear systems of equations. Under appropriate conditions, we show that the spectral residual method with this line search is globally convergent. We also present some numerical experiments. The results show that the spectral residual method with the new nonmonotone line search is promising.

Key Words: large-scale nonlinear systems; spectral residual method; nonmonotone line search


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