A Derivative-Free Method for Nonlinear System of Equations with Global Convergence

作者：Zhang, Jianguo^*; Xiao, Yun-Hai; Zhou, Dangzhen

来源：Journal of Computational Analysis and Applications, 2011, 13(7): 1319-1328.

• nonlinear system
• sufficient descent direction
• derivative-free method
• nonmonotone line search
• global convergence

In this paper, we propose a simple derivative-free method for solving large-scale nonlinear system of equations. It comes from a simple sufficient descent method [17] for unconstrained optimization problems. A remarkable property of the proposed method is that it can solve nonlinear system without requiring Jacobian matrix information. It is also suitable to large-scale equations due to its lower storage requirement. Under appropriate conditions, we show that the method with nonmonotone derivative-free line search is globally convergent. Preliminary numerical results show that the proposed method is promising.

• 出版日期2011-11
• 单位河南大学