A globally convergent derivative-free method for solving large-scale nonlinear monotone equations

Authors:
Qin-Rong Yan;Xiao-Zhen Peng;Dong-Hui Li
Affiliations:
Department of Science, Hubei Automotive Industries Institute, Shiyan, Hubei, 442002, China;Department of Science, Hubei Automotive Industries Institute, Shiyan, Hubei, 442002, China;South China Normal University, Guangzhou, 510631, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we propose two derivative-free iterative methods for solving nonlinear monotone equations, which combines two modified HS methods with the projection method in Solodov and Svaiter (1998) [5]. The proposed methods can be applied to solve nonsmooth equations. They are suitable to large-scale equations due to their lower storage requirement. Under mild conditions, we show that the proposed methods are globally convergent. The reported numerical results show that the methods are efficient.