谱HS投影算法求解非线性单调方程组

Spectral HS projection algorithm for solving nonlinear monotone equations

借助谱梯度法和HS共轭梯度法的结构,建立一种求解非线性单调方程组问题的谱HS投影算法.该算法继承了谱梯度法和共辄梯度法储存量小和计算简单的特征,且不需要任何导数信息,因此它适应于求解大规模非光滑的非线性单调方程组问题.在适当的条件下,证明了该算法的收敛性,并通过数值实验表明了该算法的有效性.

In this paper,based on the structures of spectral gradient method and HS conjugate gradient method,we propose a spectral HS projection algorithm for solving nonlinear monotone equations.The proposed algorithm inherits some advantages of spectral gradient method and conjugate gradient method such as low memory cost and simple calculation.Moreover,it does not need any derivative information,since it is very suitable to solve non-smoothly nonlinear monotone equations.Under some appropriate conditions,we prove the convergence of the proposed method,and show the efficiency of the proposed method by some numerical experiments.