求解非线性单调方程组的一种无导数投影算法

A Derivative-free Projection Algorithm for Solving Nonlinear Monotone Equations

推广了一种修正的CG_DESCENT共轭梯度方法,并建立了一种有效求解非线性单调方程组问题的无导数投影算法.在适当的线搜索条件下,证明了算法的全局收敛性.由于新算法不需要借助任何导数信息,故它适应于求解大规模非光滑的非线性单调方程组问题.大量的数值试验表明,新算法对给定的测试问题是有效的.

In this paper, we extend a modified CG_DESCENT conjugate gradient method, and establish an efficient derivative-free projection algorithm for solving nonlinear monotone equations. The global convergence of the proposed algorithm is proved by using appropriate line search. The proposed algorithm has no need for any information of derivative, so it is very suitable for solving nonsmooth nonlinear monotone equations. Numerical results show that the proposed algorithm is very efficient for some given problems.