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Journal of Applied Mathematics
Volume 2013, Article ID 286486, 7 pages
Research Article

A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints

Hunan Institute of Technology, Hengyang, Hunan 421008, China

Received 24 April 2013; Revised 5 November 2013; Accepted 5 November 2013

Academic Editor: Saeid Abbasbandy

Copyright © 2013 Sheng Wang and Hongbo Guan. 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.


Based on the Scaled conjugate gradient (SCALCG) method presented by Andrei (2007) and the projection method presented by Solodov and Svaiter, we propose a SCALCG method for solving monotone nonlinear equations with convex constraints. SCALCG method can be regarded as a combination of conjugate gradient method and Newton-type method for solving unconstrained optimization problems. So, it has the advantages of the both methods. It is suitable for solving large-scale problems. So, it can be applied to solving large-scale monotone nonlinear equations with convex constraints. Under reasonable conditions, we prove its global convergence. We also do some numerical experiments show that the proposed method is efficient and promising.