A MODIFIED SPECTRAL CONJUGATE GRADIENT PROJECTION METHOD FOR SOLVING NONLINEAR MONOTONE SYMMETRIC EQUATIONS

In this paper, an algorithm is developed to solve nonlinear monotone symmetric equations by combining a modified spectral gradient method and a projection method. The spectral and conjugate parameters in the modified spectral gradient method are chosen such that the search direction is always sufficiently descent as well as being close to the Newton direction. Under some mild assumptions, global convergence is established. In virtue of the derivative-free property and the lower storage requirement, the developed algorithm is suitable for solution of large-scale nonlinear equations. By implementing the developed algorithm to solve the benchmark test problems with dimensions from 10(3) to 10(6), the obtained numerical results show that our algorithm is promising.