TY - JOUR
T1 - Spectral DY-Type Projection Method for Nonlinear Monotone Systems of Equations
AU - Liu , Jinkui
AU - Li , Shengjie
JO - Journal of Computational Mathematics
VL - 4
SP - 341
EP - 355
PY - 2015
DA - 2015/08
SN - 33
DO - http://doi.org/10.4208/jcm.1412-m4494
UR - https://global-sci.org/intro/article_detail/jcm/9847.html
KW - Nonlinear monotone system of equations, spectral gradient method, DY conjugate gradient method, Projection method, Global convergence.
AB - <p style="text-align: justify;">In this paper, we propose a spectral DY-type projection method for nonlinear monotone systems of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differentiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is derivative-free and so is very suitable to solve large-scale nonlinear monotone systems. The preliminary numerical results show the feasibility and effectiveness of the proposed method.</p>