Abstract:

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.

Key words: nonlinear monotone equations, conjugate gradient method, spectral gradient method, projection algorithm, convergence