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In this paper, we propose a self adaptive spectral conjugate gradient-based projection method for systems of nonlinear monotone equations. Based on its modest memory requirement and its efficiency, the method is suitable for solving large-scale equations. We show that the method satisfies the descent condition $F_{k}^{T}d_{k}\leq -c\|F_{k}\|^{2}, c>0$, and also prove its global convergence. The method is compared to other existing methods on a set of benchmark test problems and results show that the method is very efficient and therefore promising.

Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations